Collimating Metalenses and Technologies Incorporating the Same

ABSTRACT

Metalenses and technologies incorporating the same are disclosed. In some embodiments, the metalenses are in the form of a hybrid multiregion collimating metalens that includes a first region and a second region, wherein the hybrid multiregion collimating metalens is configured to collimate (e.g., visible) light incident thereon. In some instances the first region includes an array of first unit cells that contain subwavelength spaced nanostructures, such that the first region functions as a subwavelength high contrast grating (SWHCG), whereas the second region includes an array of second unit cell, wherein the array of second unit cells includes a near periodic annular arrangement of nanostructures such that the second region approximates the functionality of a locally periodic radial diffraction grating. Lighting devices including such metalenses are also disclosed.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application Ser.No. 62/222,553, filed Sep. 23, 2015, and U.S. Provisional ApplicationSer. No. 62/265,799, filed Dec. 10, 2015, the entire contents of whichare incorporated herein by reference.

FIELD

The present disclosure generally relates to optical components andtechnologies including the same. In particular, the present disclosurerelates to collimating metalenses and technologies including the same,such as but not limited to lighting devices.

BACKGROUND

Interest has grown in the use of laser activated remote phosphor (LARP)for technology in various lighting applications, such as automotive,projection, and other lighting applications. One reason for thatinterest is that LARP technology has the potential to enable toproduction of lighting devices that can generate significantly higherluminance than devices that utilize light emitting diodes (LEDs), atrelatively high power levels.

FIG. 1 depicts one example of a LARP system. As shown, LARP system 100includes a first light source 101 in the form of a laser. The firstlight source 101 emits rays 103 of laser light towards a dichroic beamsplitter 105. The dichroic beam splitter 105 reflects rays 103 into acollimating optic 107. The reflected rays 103 pass through and arefocused by the collimating optic 107 onto a wavelength converter 109that is present on a substrate 111. The wavelength converter 109includes a wavelength conversion material that functions to convert(e.g., via photoluminescence) at least a portion of light rays 103incident thereon to light of a different wavelength than light rays 103,in this case light rays 115. As significant heat may be generated by theconversion of rays 103 to rays 115, a heat sink 113 may be coupled tothe substrate 111 so as to facilitate the dissipation or removal ofexcess heat.

At least a portion of the rays 115 produced by wavelength converter 109are collected by the collimating optic 107 and are redirected backthrough the dichroic beam splitter 105, where they are incident on afocusing lens 121. The focusing lens 121 focuses rays 115 on othercomponents 123 of LARP system 100, such as fiber/projection optics.

LARP system 100 may also include an optional second light source 117(e.g., a laser or non-laser source), as shown. When included the secondlight source 117 may be used to emit light rays 119 that reflect off ofthe dichroic beam splitter 105 towards the focusing lens 121. Theresultant mixing of rays 119 and rays 115 may result in a correspondingchange in the color temperature or other properties of the light in theregion down field of the dichroic beam splitter 105.

Using such a configuration tens of watts of laser light (i.e., rays 103)may be pumped into a small (e.g. square-millimeter (mm²) area ofwavelength converter 109, resulting in the production of broad ornarrow-band emission of secondary light (i.e., rays 115) with arelatively low étendue and a relatively high light output (e.g., fromseveral hundred to above 10,000 lumens). LARP systems such as the oneshown in FIG. 1 may therefore considered attractive for many projectionapplications such as digital micro-mirror (DMD) modulators, fiber opticsources, and the generation of highly collimated beams.

While LARP systems have shown some promise, challenges exist that havelimited their practical implementation in various lighting applications.One such challenge is that the wavelength converters used in many LARPsystems often produce secondary light in a hemispherical (approximatelyLambertian) pattern. For the system to be efficient, the collimatingoptic in the system needs to be able to capture a large fraction of thehemispherical luminescence produced by the wavelength converter.Capturing sufficient amounts of such light with traditional collimatingoptics can be difficult, and therefore special non-imaging type optics(e.g., a tapered total internal reflection optic as shown in FIG. 1) orvery low F/number aspheric lenses (often more than one) are often usedas collimating optics in LARP systems. Those specialized optics areoften expensive, heavy, and can take up considerable space. It may alsobe necessary to place them very close to the surface of the wavelengthconversion material (e.g., less than 100-200 microns (μm)) which canmake alignment difficult.

Similar challenges exist with collimating optics used in opticalapplications outside of the context of a LARP system. For example insome LED projection systems, one or a plurality of non-laser, highluminance LEDs is/are used emit light into a hemisphere after which theemitted light is collimated by one or more collimating optics. Onemethod of collimating the light emitted by an LED is to encapsulate theLED die in a lens. Although encapsulation can improve the lightextraction efficiency of the LED, it may undesirably increase theétendue of the LED by a factor of n², where n is the refractive index ofthe lens medium. An alternative approach may therefore be needed ininstances where maintenance of étendue is desired, such as in lightprojection systems.

One such alternative approach is to use collimating optics similar tothose used in the LARP system of FIG. 1 (either alone or in combinationwith an encapsulating lens if the increased étendue can be tolerated) tocollimate light emitted by an LED. This concept is illustrated in FIG.2, which depicts one example of a collimation system 200 in which aspatially extended light source 201 (e.g., an LED) emits rays 203 oflight towards a collimating optic 205, with the light source 201 beingaligned with the optical axis 207 of the collimating optic 205. In suchinstances, however, the same challenges associated with the collimatingoptics used in a LARP system (i.e., size, weight, alignment, cost, etc.)are presented.

An interest therefore remains in the development of alternative opticsthat are suitable for use in various applications such as LARP, highluminance LEDs, point source collimation, laser-based microscopy andother applications in which high numerical aperture collimation isdesired. As will be discussed in detail below, the present disclosuregenerally relates to such alternative optics (and in particularmetalenses) which are suitable for those and other applications.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts one example of a prior art laser assisted remote phosphor(LARP) system.

FIG. 2 depicts one example of a prior art light emitting diode (LED)collimation system.

FIG. 3A depicts a generalized cross sectional structure of one exampleof a metalens consistent with the present disclosure.

FIG. 3B is a generalized illustration of the conversion of light havinga first wave front up field of a metalens to light having a second wavefront down field of the metalens.

FIG. 4 depicts one example of a LARP system including a collimatingmetalens consistent with the present disclosure.

FIG. 5 depicts one example of an LED collimation system including acollimating metalens consistent with the present disclosure.

FIG. 6 is a plot of phase delay (Δφ) of a metasurface, versus the radialdistance (r) from the optical axis of one example of a targethyperboloidal phase shift for a metalens consistent with the presentdisclosure.

FIG. 7 is a top down view of the structure of one example of amultiregion metalens consistent with the present disclosure.

FIG. 8 is a top down view of a portion of another example of a metalensconsistent with the present disclosure.

FIGS. 9A and 9B are perspective and top down views of one example of aunit cell consistent with the present disclosure.

FIG. 10 is a plot of calculated phase shift and transmission imparted toan incident visible light plane wave by a hexagonal Bravais lattice ofnanopillars consistent with embodiments of the present disclosure.

FIG. 11 is a top down view of one example of a multiregion metalensconsistent with the present disclosure.

FIG. 12 is a simulated plot of phase versus radial position for oneexample of a one dimensional (1D) metalens with a structure consistentwith that of FIG. 7.

FIG. 13 depicts results obtained from simulations performed to determinethe ability of a 1D metalens having the design of FIG. 12 to collimatelight from a point source in one dimension.

FIG. 14 depicts perspective and top down views of another example of aunit cell consistent with the present disclosure.

FIGS. 15A-15C depict alternative unit cell configurations consistentwith embodiments of the present disclosure.

FIG. 16 depicts one example of a distribution of Hexagonal Bravais unitcells consistent with the present disclosure.

FIG. 17 depicts one example of a metalens having a multiregion designconsistent with the present disclosure.

FIGS. 18(a)-(d) depict the calculated collimating performance of oneexample of a metalens design consistent with the present disclosure.

FIGS. 19(a)-(d) depict the calculated off-axis collimating performanceof one example of a metalens design consistent with the presentdisclosure.

FIGS. 20(a)-(d) show the calculated performance of an example metalensdesign consistent with the present disclosure for a normally incident450 nm plane wave.

FIGS. 20(e)-(h) show the calculated performance of an example metalensdesign consistent with the present disclosure for 580 nm light emanatingfrom the focal point.

FIGS. 21(a) and 21(b) depicts the use of a metalens consistent with thepresent disclosure for collimating an off-axis light source.

DETAILED DESCRIPTION

As noted in the background, specialized collimating optics may be usedin various optical applications such as LARP, LED collimation, etc., tocollimate light that is emitted from a light source in a distributed(e.g., hemispherical) pattern. To be efficient, the collimating opticsused therein need to capture a large fraction of the light produced bythe light source. Although that can be accomplished by using specialnon-imaging type optics (e.g., a tapered total internal reflection opticas shown in FIG. 1) or very low F/number aspheric lenses (often morethan one) as the collimating optic, such optics present variouschallenges which have limited their practical implementation in variousapplications such as LARP, LED collimation, etc. In particular, thoseoptics present size, weight, and alignment constraints that make itpractically difficult to implement LARP and LED collimating technologyin compact lighting applications such as automotive lamps, compactlighting fixtures, compact projection systems, and the like. Effortshave therefore been made to reduce the size, cost, and/or weight ofcollimating optics, so as to facilitate the implementation of LARP andLED collimating technology in those lighting applications.

The inventors have considered various options for replacing thespecialized collimating optics often used in LARP and LED collimationsystems. One option that has been considered is the Fresnel lens.Although Fresnel lenses are well understood optical designs, practicallyimplementing a Fresnel lens that exhibits desirable properties for LARP,high luminance LED, and point source collimation has proven challenging.Indeed while it is theoretically possible to design a Fresnel lens thatexhibits suitable properties for such applications, physically producingsuch lens can be practically difficult. Indeed the production of Fresnellenses often entails the use of precision molding and polishing toachieve high quality focusing and/or collimation, particularly whenenvironmental considerations encountered in LARP and/or LED collimation(e.g., exposure to high heat and high short wavelength fluxes) dictatethe use of glass as a lens material, instead of plastic. Fresnel lensescan therefore be difficult and expensive to produce, and are often notcost effective for a variety of applications. Some Fresnel lens designsalso can give rise to optical artifacts, scattering loss, andaberrations, particularly if the lens is designed to have a short focallength, a feature that is often desired in collimating optics for LARPand LED collimation.

Flat diffractive optics have also been considered as an option forreplacing the specialized collimating optics used in LARP, LEDcollimation, and other applications. For example, it is possible todesign a flat diffractive optic that induces a spatially dependent phasemodulation on light incident thereon, e.g., by designing the optic suchthat the phase change induced at its surface only needs to vary between0 and 2π to achieve a desired wave front. Such optics can be producedusing various approaches, such as with a zone plate, the diffractivelimit of a Fresnel lens, or kinoform. Lithography, photo curing, andeffective medium approaches may also be leveraged to produce a desiredphase change. However all of those options can present significantfabrication challenges in the context of producing a lens that exhibitsproperties that may be considered desirable for application in LARPand/or LED collimation.

With the foregoing in mind, the inventors have identified metasurfacelenses (hereinafter, “metalenses”) as a class of optics that may beadvantageously leveraged as a replacement for the collimating opticsused in various challenging optical applications, such as LARP, LEDcollimation, and laser based spectroscopy.

As used herein, the terms “metasurface lens” and “metalens” are usedinterchangeably to refer to a lens that bends light with an array ofnanostructures that are formed on a (ideally flat) surface of asubstrate, instead of via refraction. More specifically, a metalensincludes a metasurface that includes an array of nanostructures, whereinthe nanostructure array is configured to bend light incident thereon byaltering its phase. As will be described, the phase change imparted bythe metasurface can create a new wave front in a region down field ofthe lens. For example, a metalens consistent with the present disclosurecan include an array of nanostructures that can impart a phase change toincident light having a spherical or hemispherical wave front up fieldof a lens, such that the light in a region down field of the lens has aplanar wave front (i.e., a plane wave).

As used herein the term “point light source” refers to a light sourcethat is an ideal infinitesimal region that emits a spherical orhemispherical wave of light. Single mode optical fiber light sources areone example of a light source that can approximate a point light source.With that in mind, the present disclosure discusses the use ofmetalenses in the context of certain applications such as LEDcollimation and wavelength converted LARP. Such applications utilize oneor more LEDs and/or a wavelength converter (e.g., a ceramic phosphorplate) which are extended sources which emit from a finite area. Inthose contexts, one can consider an LED or a wavelength converter to bean incoherent superposition of ideal point sources which cover theemitting area of the extended source. Moreover due to the small physicalsize of a wavelength converter in LARP or a high luminance LED source inan LED collimator, one may consider them to be close to a point sourcefrom the geometric optics point of view, provided that all other lengthscales in the optical system are much larger than the source sizes.

In the context of the present disclosure, the term “on,” when used inthe context of describing a positional relationship between components,means that a first component is disposed above a second component, butis not necessarily in direct contact with the second component. Incontrast, the term “directly on,” when used in that same context meansthat a first component is in direct contact with the second component.

As used herein the term “about” when used in connection with a value ora range, means +/−5% of the indicated value or the endpoints of theindicated range. It is noted that while ranges may be specified hereinby specific endpoints, such ranges should be understood to a shorthandversion of writing all of the numerical values within that range. Thusfor example, a range of 1-10% should be understood to all of thenumerical values within that range (i.e., 1, 2, 3, 4, etc.), as well asall ranges that may be defined by two or more values within than range(e.g., 2-10%, 3-10%, 4-8%, etc.) as though such values and ranges wereexplicitly recited.

FIG. 3A depicts one example of a generalized cross sectional structureof a metalens structure consistent with the present disclosure. Asshown, metalens 301 includes a substrate 303 having a first side 309 anda second side 311. A metasurface 305 is formed on the first side 309 ofthe substrate 303. In some embodiments, an optional antireflectivecoating 307 is formed on the second side 311 of the substrate 303. Asdiscussed herein the metasurface 305 includes an array of nanostructures313, which are generally configured to impart a phase change to lightincident thereon.

Substrate 303 generally functions to support other elements of metalens301, such as but not limited to metasurface 305 and optionalantireflective coating 307. The substrate 303 may also be selected totransmit a suitable amount of light of a desired wavelength orwavelength range, such as one or more wavelengths in the visible regionof the electromagnetic spectrum (i.e., from about 400 to about 700nanometers). Without limitation, in some embodiments the substrate 301is configured such that it transmits greater than or equal to about 50%,60%, 70%, 80%, 90%, 95%, 99%, or even about 100% of light in the visibleregion of the electromagnetic spectrum. Without limitation, in someembodiments substrate 303 transmits greater than or equal to about 95%of visible light incident thereon.

Substrate 303 may be formed from any suitable material, provided that itcan adequately transmit light in a desired wavelength or wavelengthrange (e.g., visible light) and can serve as an adequate support formetasurface 305 and (where used) optional antireflective coating 307. Insome embodiments, the material of substrate 301 has a refractive indexthat is relatively low, as compared to the refractive index of materialsused in metasurface 305. Non limiting examples of suitable transparentmaterials that may be used as substrate 303 include aluminum oxide(Al₂O₃) silicon dioxide (SiO₂), polymers, combinations thereof, and thelike. Such materials may be crystalline or amorphous (glassine). Glassesmay be desirable because of cost, ease of polishing, and lack ofbirefringence.

Metasurface 305 generally functions to alter the phase of light that isincident thereon, such light down field of the lens (relative to thelight source) has a desired distribution and/or wave front. For example,in some embodiments metasurface 305 is configured to convert lighthaving a first wave front (e.g., a spherical, hemispherical, etc.) in anregion up field of the lens to light having a second (e.g., planar) wavefront in a region down field of the lens.

FIG. 3B illustrates a generalized example of that concept. As shown inthat figure, a metalens 301 is positioned proximate to a point lightsource 315, such as a wavelength converter used in LARP, an LED, or thelike. Regardless of its specific form, point light source 315 emitslight in a hemispherical wave front towards one side of metalens 301,i.e., in a region up field (UFR) of metalens 301. The light in the UFRmay therefore be understood to have a spherical or hemispherical wavefront 317. Light incident on metalens 301 propagates through substrate303 and is incident on metasurface 305 or, more particularly, on anarray of nanostructures 313 in metasurface 305. As shown in thissimplified example, the nanostructures 313 of metasurface 305) convertthe incident spherical wave front 317 into light having a planar wavefront 319 in a region down field (DFR) of metalens 301. In that way,metalens 301 can produce a collimated light beam of parallel light raysfrom an incident spherical or hemispherical wave front.

When used, the optional antireflective coating 307 generally functionsto reduce reflection of light that is incident on or which is exitingfrom metalens 301 depending on whether the incident light enters on thesubstrate side (i.e., side 311) or the metalens side (i.e., side 309).It is noted that while FIG. 3A depicts an embodiment of a metalens 301in which optional antireflective coating 307 is disposed on the secondside 311 of substrate 303 (i.e., opposite the first side 309 bearing themetasurface 313), use of the optional antireflective coating 307 on thesecond side 311 is not required. For example, in some embodiments theoptional antireflective coating 307 is disposed on (e.g., directly on)the metasurface 305. In any case, a variety of materials may be used asor in optional antireflective coating 307. Non-limiting examples of suchmaterials include transparent dielectric materials, such as but notlimited to SiO₂, TiO₂, MgF₂, Ta₂O₅, Nb₂O₅, combinations thereof, and thelike.

Returning to the metasurface 305, the nanostructures 313 in metasurface305 are generally configured to function as resonators or waveguidesthat impart a phase change to light incident thereon. In that way, thenanostructures 313 can convert light having a first wave front in aregion up field of the metalens 301 to light having a second wave frontin a region down field of the metalens 301. For example, nanostructures313 can impart a phase change to light in an incident hemispherical wavefront 317, so as to produce light having a planar wave front 319 (i.e.,collimated light) in a region down field of metalens 301.

It is noted that while FIG. 3B depicts metasurface 305 down field of theincident spherical wave front 317 (i.e., further from the point lightsource 315), such a configuration is not required and metasurface 305may be present on the other or both surfaces of substrate 301. Forexample, metasurface 305 in some embodiments may be present on bothsides of substrate 301, like a biconvex lens, in which the collimatingpower of the metalens 301 may be divided between the two metasurfaces.

Metasurface 305 includes or is formed from an array of nanostructures313. In general, nanostructures 313 are in the form of nanoscalefeatures that are formed on (e.g. directly on) or are integral with asurface of substrate 301. As used herein, the term “nanoscale” when usedin connection with a feature means that the dimensions of the featuresare less than 1 micron. In general, the dimensions of the nanostructures313 will scale with the shortest wavelength of interest. In the contextof the present disclosure, which is largely directed to visible lightapplications for metalenses, the largest linear dimension of thenanostructure in the plane of the substrate surface (e.g., length,width) is less than or equal to 500 nanometers (nm), such as less thanor equal to 150 nm, or even less than or equal to 100 nm. Withoutlimitation, in some embodiments the nanostructures 313 described hereinare nanoscale structures formed on a surface of substrate 301, and havea longest linear dimension of about 100 to about 200 nanometers. In someinstances the largest linear feature size of nanostructures 313 is theirheight relative to the surface of substrate 303 proximate thenanostructure 313 in question. In such instances the height of thenanostructures 313 may be less than or equal to 1000 nm, such as lessthan or equal to 600 nm. It noted however that the height of thenanostructures is not limited to those ranges, and that their height maybe larger than 1 micron if desired.

The distance (i.e., “period” or “fundamental period”) between adjacentnanostructures 313 in the metasurfaces may vary widely, and may beselected during the design of metalens 301 to facilitate the attainmentof a desired phase change at a particular portion of the lens. Withoutlimitation, in some embodiments the period between adjacentnanostructures 313 ranges from about 50 to about 1000 nanometers (nm),such as from about 100 to about 500 nm, about 100 to about 300 nm, oreven about 100 to about 200 nm. In some embodiments the period betweenadjacent nanostructures 313 in metasurface 305 is greater than or equalto 100 nm to facilitate production of metasurfaces 305 via lithographicor other techniques. In instances where nanostructures are included in aBravais lattice (e.g., a hexagonal Bravais lattice) formed by unit cellscontaining a plurality of nanostructures, the period of thenanostructures may correspond to one or more lattice parameters of theunit cell(s) used to form the lattice.

For the sake of clarity and ease of understanding, the presentdisclosure will describe various examples of metalenses that includenanostructures 313 in the form of cylindrical pillars that are formed onthe surface of a substrate 301. It should be understood that the use ofcylindrical pillars is for the sake of example only, and thatnanostructures 313 are not limited to a cylindrical pillar shape.Indeed, the shape of the nanostructures described herein can varyconsiderably. For example, the metasurfaces described herein may includean array of nanostructures 313, wherein the nanostructures are in theform of cylindrical pillars, ellipsoidal pillars, spheres, rectangularprisms, other scattering structures, or the like. When thenanostructures described herein are in the form of pillars, such pillarsmay have one or more than one side. Examples of such pillars includecylindrical (one sided) pillars, triangular (three sided) pillars,quadrilateral (four sided pillars), pentagonal (five sided) pillars, andthe like.

As noted previously the dimensions of the nanostructures describedherein may vary considerably. For example in some embodiments themetasurfaces described herein include an array of nanostructures,wherein the height of such nanostructures is fixed or variable acrossthe entirety or a portion of a metalens. In any case, the height of thenanostructures may be in the range of from about 50 to about 2000 nm,such as about 100 nm to about 600 nm, or even about 100 to about 200 nm.In some embodiments, the height of the nanostructures is greater than100 nm. Of course such ranges are enumerated for the sake of exampleonly, and the nanostructures herein may be of any suitable height.

The lateral size of the nanostructures described herein may also varyconsiderably. For example in instances where the nanostructures are inthe form of cylindrical nanoscale pillars, such pillars may have acenter and a radius extending from the center to an outer wall of thepillar. The radius of such pillars may range, for example, from about 25to about 500 nm, such as from about 50 to about 250 nm, or even about 50to about 100 nm. Without limitation, in some embodiments thenanostructures are in the form of cylindrical pillars having a diameterof greater than or equal to about 50 nm. Similarly in instances wherethe nanostructures include or are in the form of multisided pillars orother geometric shapes, such structures may have a lateral length (i.e.,a longest linear dimension as measured between opposing sides of ananostructure) ranging from about 50 to about 2000 nm, such as about 100nm to about 600 nm, or even about 100 to about 200 nm. Of course suchranges are enumerated for the sake of example only.

A wide variety of materials may be used to form the nanostructures 313.In some instances, it may be desirable to select the materials forforming the nanostructures 313 based on the wavelength(s) of light thatwill be incident on the metalens 301 in a target application. When atarget application involves using the metalens 301 to impart a phasechange to visible light, for example, it may be desirable to form thenanostructures 313 from one or more materials that interact with visiblelight. Non-limiting examples of such materials include high refractiveindex, low loss dielectric materials such as dielectric oxides (TiO₂,Nb₂O₅, Ta₂O₅, ZnO), carbides (e.g., SiC), diamond, sulfides (e.g., ZnS,CdS, and/or nitrides (e.g., AlN). Alternatively or additionally, thenanostructures 313 may be formed from or include one or more high-indexpolymers (n>1.6), such as but not limited to silicones and/or acrylics.Polymers with even higher index may also be used, and may be formed, forexample, by highly loading a polymer matrix with nanoparticles that havea refractive index of greater than or equal to 1.8, or even greater thanor equal to 2. In some embodiments, the materials used to form thenanostructures 313 are transparent to light in the region of interest(e.g., visible light), and exhibit an absorptivity of less than 100/mm.

The nanostructures described herein are not limited to a singlematerial, and may be formed from more than one material. For example,the nanostructures may include two or more of the above noted materials,wherein alternating layers (or other configurations) of such materialsare used to “build up” a nanostructure on the surface of a substrate.Lithographic and other techniques to produce such structures are wellunderstood.

The refractive index of the materials used to form the nanostructures313 may impact their performance for a given application. It maytherefore be desirable to select materials for forming thenanostructures 313 based on their refractive index. In that regard, insome embodiments the nanostructures 313 may be formed from or includedielectric or other materials having an refractive index that is greaterthan or equal to about 1.5, 2.0, 2.3, 2.5, 2.7, or more. Withoutlimitation, in some embodiments nanostructures 313 are formed from orinclude dielectric materials having a refractive index greater than orequal to 2. Non-limiting examples of such materials include thosementioned above.

The relationship between the refractive index of nanostructures 313 andsubstrate 303 may also affect the performance of metalens 301. It maytherefore be desirable to select the materials used to form substrate303 and nanostructures 313 such that they have a particular refractiveindex relationship. In that regard the refractive index of thenanostructures 313 may be greater than, less than, or equal to therefractive index of substrate 303. Without limitation, in someembodiments the refractive index of nanostructures 313 is greater thanthe refractive index of substrate 303. It is noted, that by usingnanostructures 313 that have a refractive index greater than therefractive index of substrate 303, it is possible to reduce or minimizethe amount of high angle scattered light that may be trapped in thensubstrate 303 due to total internal reflection. Moreover, selecting thematerials of the substrate 301 and the nanostructures 313 formed thereonsuch that there is a large difference in the refractive index of thenanostructures 313 and the substrate 301 can also be beneficial, as itcan provide some resonance or cavity enhancement effects within thenanostructures 313, resulting in the production of larger phase shiftsfor a given length.

The microstructure of the materials used as nanostructures 313 may alsohave an impact on their optical performance. For example, in someinstances the microstructure of the materials used to formnanostructures 313 may give rise to artifacts in light down field of thelens. Alternatively or additionally, the microstructure of the materialsof nanostructures 313 can cause anisotropic propagation of light throughmetalens 301. It may therefore be desirable to select materials for useas nanostructures 313 based on their microstructure. For example, it maybe desirable to use amorphous or cubic materials (e.g., amorphous TiO₂,cubic ZnO), so as to control anisotropic propagation effects in metalens301. Of course, it is not necessary to use amorphous or cubic materialsto form nanostructures 313, and materials with other microstructures mayalso be used. It is noted that nanostructures consistent with thepresent disclosure need not have a uniform (i.e., single) nanostructure,and that such structures may include a composite, random, or othercomplicated microstructure, as desired. However, the materials used toform the nanostructures 313

In specific non-limiting embodiments, metalens 301 includes a substrate303 formed from quartz, silica (SiO₂) or alumina (Al₂O₃), and thenanostructures 313 are formed from or include titanium dioxide (TiO₂) orzinc oxide (ZnO). In further examples the substrate 303 is formed fromquartz, SiO₂ or Al₂O₃, and the nanostructures 313 are formed fromamorphous TiO₂ or cubic ZnO. In any of those specific non-limitingembodiments, the nanostructures 313 may be in the form of include anarray of cylindrical pillars, e.g., with a largest linear dimension(e.g., height) in the range of about 100 to about 2000 nm. The lateraldimensions (in the plane of the substrate) in some embodiments areconstrained by the wavelength of light, and are often less than or equalto one half (½) of the wavelength of light.

From FIG. 3B it can be appreciated that the path length of rays emittedfrom the point light source 315 in a spherical wave front 317 increasesas one moves radially outward from the optical axis 350 (assuming thepoint light source 315 is at the focus of the metalens 301). Similarly,the angle of incidence at which light in the incident spherical wavefront 317 impinges on metalens 301 generally increases as one movesradially outward from the optical axis 350. It may therefore be desiredto control the degree to which the array of nanostructures 313 in themetasurface 305 alters the phase of incident light, based at least inpart on the position on which the light is incident relative to theoptical axis 350 of the metalens 301. Put in other terms, it may bedesirable to configure the array of nanostructures 313 such that thephase delay imparted by such structures to a light in an incidenthemispherical wave front 315 is dependent on the radial position ofthose nanostructures relative to the optical axis 350 of the lens.

In some embodiments therefore the array of nano structures 313 in themetasurface 305 is configured to compensate for the difference inoptical path length and/or angle of incidence as one moves radiallyoutward from the optical axis 350. This may be accomplished, forexample, by varying aspects of the geometry (e.g., height, width,radius, etc.) of the nanostructures 313, either independently, in thecontext of a unit cell containing a plurality of nanostructures 313, oreven in the context of an array containing a plurality of unit cells.

For example, during the design process the metasurface 305 may besubdivided into a plurality of two dimensional (2D) unit cells, whereineach unit cell includes a plurality of nanostructures 313. The unitcells may have any suitable geometry, and may be symmetrical orasymmetrical. Without limitation, in some embodiments all or at least aportion of the shape of the unit cells and their contents aresymmetrical (e.g. square, hexagonal, triangular, etc.), so as to reduceor eliminate polarization dependent effects. A plurality of such unitcells may be used to make up one or more regions of the metasurface 305.In such instances the geometry of each unit cell (e.g., length, width,etc.) and/or the nano structures 313 therein (e.g., nanostructureheight, width, diameter, position within a unit cell, etc.) may becontrolled such that the nanostructures 313 in each respective unit cellimparts an appropriate phase change to incident light, based at least inpart on the position of the unit cell relative to the optical axis 350of metalens 301.

Through appropriate design of the metasurface 305 (or, moreparticularly, nanostructures 313 and/or unit cells containing suchnanostructures), it is possible to design metalenses that exhibit usefuloptical properties for visible light applications such as LARP and LEDcollimation. Such properties include but are not limited to highnumerical aperture (NA), short focal length, polarization insensitivity,and/or high lens transmission (e.g., in the visible region).

As used herein, the term “high numerical aperture” means a numericalaperture that is greater than or equal to about 0.5. Therefore in someembodiments the metalenses described herein may exhibit a NA that isgreater than or equal to about 0.5, such as greater than or equal toabout 0.6, greater than or equal to about 0.7, greater than or equal toabout 0.8, greater than or equal to about 0.9, or even greater than orequal to about 0.95.

As used herein, the term “short focal length” means a focal length thatis less than or equal to about 5 millimeters (mm). Therefore in someembodiments, the metalenses described herein have a focal length that isless than or equal to about 5 mm, less than or equal to about 4 mm, lessthan or equal to about 3 mm, less than or equal to about 2 mm, less thanor equal to about 1 mm, less than or equal to about 0.5 mm, or even lessthan or equal to about 0.2 mm. Without limitation, in some embodimentsthe metalenses described herein have a focal length of less than orequal to about 1 mm.

As used herein, the term “lens transmission” means the percentage oflight that is within the lens numerical aperture that is transmittedthrough the lens into a collimated beam down field of the lens. In someembodiments the metalens described herein have a lens transmission forlight in the visible range that is greater than or equal to about 50%,such as greater than or equal to about 60%, about 70%, about 80%, about90%, or even about 99%. Without limitation, in some embodiments themetalenses described herein have a metalens transmission of greater thanor equal to about 80% for light in the visible range.

In some embodiments the metalenses described herein exhibit acombination of high numerical aperture, short focal length, and highlens transmission for light in the visible range. For example, in someembodiments the metalenses described herein have a numerical aperturethat is greater than or equal to 0.5, a focal length of less than orequal to about 2 mm, and have a lens transmission greater than or equalto 50% for visible light. In further non-limiting embodiments,metalenses consistent with the present disclosure have a numericalaperture that is greater than or equal to 0.8, a focal length of lessthan or equal to about 1 mm, and have a lens transmission of greaterthan or equal to 80% for visible light.

The overall geometry of the metalenses described herein may vary widely.For example, the metalenses described herein may be in the form of asubstantially flat, one-dimensional (1D) lens (analogous to atraditional refractive cylindrical lens), a two-dimensional (2D) lens(analogous to a traditional refractive spherical and aspherical lens),or, by application of the metalens structures on both sides of thesubstrates, in the form of a functional equivalent of a traditionalrefractive bi-convex, bi-concave, or convex-concave lens. A hybridrefractive metalens may also be formed by the use of a substrate havingone or more curved surfaces.

Without limitation, in some embodiments metalens 301 is in the form of asubstantially flat, two-dimensional (2D) lens. As used herein, the term“substantially flat” when used in the context of a 2D lens means thatthe average surface roughness (Ra) of the lens is less than about 10 nm,such as less than about 5 nm, or even less than about 2 nm. Putdifferently, in some embodiments the overall surface roughness of themetalens is less than wavelength/10, so as to limit or prevent theintroduction of phase errors.

The overall dimensions of the metalenses described herein may varywidely, and metalenses of any suitable size may be used. In instanceswhere the metalenses is a 2D circular lens, for example, such lenses mayhave a diameter ranging from about 0.2 mm to about 3 centimeters (cm) ormore, such as from about 1 mm to about 5 mm.

In some embodiments the metalenses described herein function to focuslight incident on one side thereof and (by reciprocity) to collimatelight incident on another side thereof. For example and with referenceto FIG. 3A, the metalens 301 may (through appropriate configuration ofmetasurface 305), be configured to focus light that is incident on afirst side thereof and to collimate light that is incident on a secondside thereof. In some embodiments the first side is the side of metalensto which the first side 309 of substrate 303 is oriented, whereas thesecond side is the side of metalens 301 to which the second side 311 ofsubstrate is oriented. Of course metasurface 305 need not be configuredin that manner. For example, in some embodiments metasurface 305 may beconfigured to collimate light that is incident on the first side 309 ofmetalens 301, and to focus light that is incident on the second side ofmetalens 301, wherein the first and second sides of metalens are definedas previously described.

As noted above, the inventors have discovered that through appropriateconfiguration of a metasurface, it is possible to produce metalensesthat exhibit a combination of properties that render them attractive foruse in a variety of lighting applications, such as LARP, LEDcollimation, laser based spectroscopy, and the like. For example themetalenses described herein can exhibit a combination of short focallength and high numerical aperture. It is therefore possible to use suchlenses as a collimating optic in a LARP system, wherein the metalens isplaced at a distance (d) from the wavelength converter, where d is thesame as or different from the focal length (f) of the metalens. This canallow a dichroic mirror to be placed quite close to the metalens,resulting in a highly compact reflective LARP system in which themetalens can produce a highly collimated beams from an incidenthemispherical/spherical wave front while maintaining étendue. Similaradvantages can be obtained in other LARP configurations, such astransmissive LARP (e.g., where primary light is incident on one side ofwavelength converter, secondary light is emitted on the other side ofthe wavelength converter, and a collimating metalens collimates thesecondary light) and reflective LARP using off-axis illumination.Moreover, similar advantages can be attained using the metalensesdescribed herein as a collimating optic for LED collimation, collimationof near-point sources (output from a single mode or small diametermulti-mode fiber) optic and other systems.

Another aspect of the present disclosure is a laser assisted remotephosphor (LARP) system that includes a metalens consistent with thepresent disclosure as a collimating optic (also referred to herein as acollimating metalens). Reference is therefore made to FIG. 4, whichdepicts one example of a LARP system 400 consistent with the presentdisclosure. As shown, LARP system 400 includes a collimating metalens401, a first light source 402, a dichroic beam splitter 405, and a LARPtarget that includes a wavelength converter 409, a substrate 411, and aheat sink 413. Although one or ordinary skill will understand that othercomponents can also be included in LARP system 400 (e.g., mirrors,driving circuits, heat sinks, etc.), such components have been omittedin the interest of brevity and ease of understanding.

In operation the first light source 402 emits primary light rays 403towards the dichroic beam splitter 405. The dichroic beam splitter 405reflects the rays 403 towards the collimating metalens 301. In thisapplication the collimating metalens 401 includes a metasurface and asubstrate that are configured to transmit the primary light rays 403such that they are incident on the wavelength converter 409. Themetalens 401 in this application is designed to provide differentfocusing properties of the primary light rays 403 than would occur withthe secondary light rays 415. This provides a degree of flexibility thatcannot be obtained with traditional refractive optics or diffractiveoptics. In some respects, the metalens 401 can act as a wavelengthdependent optic or kind of notch filter for all or a portion of theprimary light rays 403, while focusing or collimating the secondarylight rays 415 and having little influence on unconverted primary lightthat may be redirected back through the metalens 401. Otherwisecollimating metalens 401 is configured and operates in much the samemanner as described herein with regard to the metalens 301 of FIG. 3and/or the multiregion metalenses described later. Without limitation,in some embodiments the metalens 401 is a multiregion metalens.

After passing through the metalens 401 the primary light rays 403 areincident on wavelength converter 409. Generally, the wavelengthconverter functions to convert the primary light rays 403 to secondarylight rays 415, e.g., via photoluminescence. The secondary light rays415 emitted by the wavelength converter 409 are of a wavelength orwavelength range that differs from the (first) wavelength of primarylight rays 403.

The wavelength converter 409 emits the secondary light rays 415 in afirst light distribution (e.g., a hemispherical (Lambertian)distribution), such that a first (e.g., spherical, hemispherical, etc.)wave front of secondary light rays 415 is incident on the metalens 401.As shown, the distance between the metalens 401 and a surface of thewavelength converter 409 may correspond to the focal length (f) of themetalens 401, but it should be understood that this is not required.Consistent with the prior discussion, f may be less than or equal toabout 5 mm, 4 mm, 3 mm, 2 mm, less than or equal to about 1 mm, lessthan or equal to about 0.5 mm, or even less than or equal to about 0.2mm. Without limitation, in some embodiments f is less than or equal toabout 1 mm.

As discussed herein the metalens 401 includes a metasurface that isconfigured to convert the first (e.g., spherical, hemispherical, etc.)wave front of secondary light rays 415 into a second (e.g., planar) wavefront, such that the secondary light rays 415 are collimated in a regiondown field (DFR) of metalens 401, relative to wavelength converter 409.The metalens 401 may also be configured to exhibit a combination of highnumerical aperture (NA), short focal length (f), and high lenstransmission for the secondary light rays 415. For example, the metalens401 in some embodiments has an NA greater than or equal to 0.5 (e.g.,≧0.8), a focal length f of less than or equal to 2 mm (e.g., f≦1 mm),and has a lens transmission greater than or equal to 50% for thewavelength(s) of the secondary light rays 415. Alternatively in someembodiments the metalens 401 in some embodiments has an NA greater thanor equal to 0.9, a focal length f of less than or equal to 2 mm (e.g.,f≦1 mm), and has a lens transmission of greater than or equal to about80% for the wavelength(s) of the secondary light rays 415. Of course,metalens 401 can exhibit other (e.g., higher) numerical aperture, aswell as different lens transmission.

The collimated secondary light rays 415 pass through the dichroic beamsplitter 405 and are focused by lens 421 onto other optics 423 (e.g.,fiber optics, projection optics, etc.) of the LARP system 400. Ifdesired, an optional second light source 417 may be used to addadditional color channels 419 that reflect off of the dichroic beamsplitter 405 to be focused on the additional optics 423 by the lens 421,as shown.

The first light source 402 may be a laser light source that isconfigured to emit primary light rays 403 of any suitable wavelength,provided that they can be reflected off of dichroic beam splitter 405and transmitted through the metalens 401, as generally shown in FIG. 4.For example, in some embodiments the light source 402 is a laser thatemits primary light rays 403 in the violet, blue, green, yellow, red, orother portion of the visible region of the electromagnetic spectrum.Without limitation, in some embodiments first light source 402 is a bluelaser that emits primary light rays 403 having a wavelength ranging fromabout 430 to about 470 nm. Alternatively, the light source 402 may be adiode laser or other light source that emits primary light rays 403 inthe near ultra-violet and/or ultra-violet regions, ranging from 375nm-420 nm. Alternatively, the light source 402 may emit visible light inrange of about 470 to about 670 nm. As will be appreciated, thewavelength of primary light rays 403 and the composition of wavelengthconverter 409 may vary considerably, and may be chosen in combinationbased on the desired application.

As noted previously in the embodiment of FIG. 4 the metalens 401 isconfigured with a notch filter characteristic, such that it transmitslight of the wavelength(s) of the primary light rays 403. Therefore whenthe primary light rays 403 are blue laser light with a wavelength in therange of 430 to about 470 nm (e.g., 440 nm, 460 nm, etc.), the metalens401 is configured with a notch filter characteristic for light in therange of about 430 to about 470 nm (e.g., 440 nm, 460 nm, etc.).

The wavelength converter 409 generally functions to convert incidentprimary light rays 403 to secondary light rays 415. In that regard, insome embodiments the wavelength converter 409 is formed from or includesone or more photo luminescent materials that are capable of convertingincident primary light rays 403 to secondary light rays 415.Non-limiting examples of suitable photo luminescent materials that maybe used include cerium activated garnets of the general formula (Y, Lu,Gd)₃Al₅O₁₂:Ce (e.g., Y3Al₅O₁₂:Ce (Ce:YAG), Lu₃Al₅O₁₂:Ce (Ce:LuAG), and(Y, Gd)₃Al₅O₁₂:Ce (CE:GdYAG), europium activated oxynitrides of thegeneral formula (Ba, Ca, Sr)Si₂O₂N₂:Eu (e.g., (SrSi₂O₂N₂:Eu (Eu:SrSiON),and various other phosphor materials known in the art. Withoutlimitation, in some embodiments wavelength converter 409 is or includesone or more of Ce:YAG, Ce:LuAG, Ce:GdYAG, or Eu:SrSiON. In someembodiments the wavelength converter 409 is a ceramic phosphor plate,meaning that it is a solid, sintered polycrystalline photo luminescentmaterial, e.g. of one or more of the materials identified above as beingsuitable for use in the wavelength converter 409.

As shown in FIG. 4 the wavelength converter 409 is coupled to asubstrate 411, which in turn is coupled to a heat sink 413. Withoutlimitation, the wavelength converter 409 in some embodiments is aceramic phosphor platelet that is bonded to a high reflectivitysubstrate 411 with an optional high thermal conductivity adhesive (notshown). When used, the high thermal conductivity adhesive may be formedany suitable high thermal conductivity material, such as alumina, zincoxide filled silicone, low temperature glasses, and the like.Alternatively or additionally, the wavelength converter 409 may be aceramic phosphor that is coated with a highly reflective coating, andwhich is soldered to the heat sink 413. The heat sink 413 generallyfunctions to remove excess heat that may be produced by wavelengthconverter 409 during the conversion of primary light rays 403 tosecondary light rays 415.

As discussed above the metalens 401 can exhibit desirable opticalproperties for LARP, but may be relatively small compared to specializedcollimating optics previously used for LARP applications. For example,the metalens 401 may be a circular 2D lens having a diameter rangingfrom about 0.2 mm to about 3 centimeters (cm), such as from about 1 mmto about 1 cm, or even about 1 mm to about 5 mm. The other components ofLARP system 400 may be correspondingly reduced in size, resulting in acompact LARP system that can be used in various compact lightapplications.

Another aspect of the present disclosure relates to lighting devicesthat include a LARP system that includes a collimating metalens. Thisconcept is shown in FIG. 4, which depicts the LARP system 400 as beingoptionally included in a lighting device 495. Non-limiting examples oflighting devices that may be used as lighting device 495 includeautomotive lighting fixtures (e.g., headlamps, turn signals, fog lamps,etc.), interior and exterior lighting fixtures (e.g., overhead lightingfixtures, luminaires, spotlights (e.g., PAR spotlights), securitylighting, etc.), industrial lighting, flashes for smart phone and othercameras, fiber optic sources (microscopes), collimating light from anoptical fiber, combinations thereof, and the like. Without limitation,in some embodiments lighting device 495 is a compact light device, suchas but not limited to an automotive headlamp, automotive tail lamp,automotive turn signal, automotive interior light, automotive spotlight, automotive fog light, or the like. In some embodiments, lightingdevice 495 is an automotive headlamp.

Another aspect of the present disclosure relates to a collimation systemin which a metalens consistent with the present disclosure is used as acollimating optic. More specifically, one aspect of the presentdisclosure relates to an LED collimation system in which a collimatingmetalens is used to collimate light from one or more LEDs, such as achip level or remote phosphor conversion LED. In that regard referenceis made to FIG. 5, which depicts one non-limiting example of thestructure of a collimation system consistent with the presentdisclosure. As shown, collimation system 500 includes a collimatingmetalens 501 and a light source 502. Although one or ordinary skill willunderstand that other components can be included in the collimationsystem 500 (e.g., mirrors, driving circuits, heat sinks, etc.), suchcomponents have been omitted from FIG. 5 in the interest of brevity andease of understanding.

Similar to the wavelength converter 409, the light source 502 isgenerally configured to emit light rays 503 of a given wavelength orwavelength range into a region up field (UFR) of the metalens 501.Unlike the wavelength converter 409, however, emission of the light rays503 by the light source 502 from a light emitting surface thereof, e.g.,in response to the application of a driving electric current.

The light source 502 is aligned along the optical axis 507 of themetalens 501 and may emit light rays 503 in any region of theelectromagnetic spectrum, such as the ultra-violet, visible, and/orinfrared regions. Without limitation, in some embodiments the lightsource 502 is configured to emit light rays 503 in the visible region ofthe electromagnetic spectrum.

Regardless of the wavelength of the light rays 503, the light source 502is configured to emit a distribution of such rays into a region up field(UFR) of the metalens 501. The light rays 503 have a first distributionand a first wave front in the UFR. The light rays 503 are then incidenton a metasurface (not shown) of metalens 501 or, more particularly, onan array of nanostructures in that metasurface.

Like the metasurfaces of the previously described metalenses, themetasurface of the metalens 501 is configured to impart a phase changeto the light rays 503, such that the light rays 503 are collimated in aregion down field of the metalens 501 (DFR) and have a second wave frontthat differs from the first wave front of the light rays 503 in the UFR.For example, in instances where the light rays 503 have a spherical orhemispherical wave front in the UFR, the metasurface may be configuredto impart a phase change to the light rays 503 such that they arecollimated and have a have a planar wave front in the DFR. In that way,the metalens 501 can produce a collimated light beam of parallel lightrays 503 in the DFR.

The metalens 501 in FIG. 5 (i.e., for extended source collimationapplications) generally functions in much the same manner as the othermetalenses described herein, such as metalenses 301 and 401 in FIG. 3and FIG. 4 (e.g., for LARP applications), and the multiregion metalensesdescribed later. A detailed discussion of the structure and function ofthe metalens 501 is therefore not reiterated for the sake of brevity.One notable exception is that unlike metalenses for LARP applications(e.g., metalens 401), the metalens 501 does not need to be configured totransmit pump (primary) light that is emitted from a first light source(e.g., a laser), such that the primary light is incident on a wavelengthconverter. Therefore for extended source collimation systems such as theone shown in FIG. 5, it is not necessary to configure at least a portionof the metasurface of the metalens 501 with notch bandpasscharacteristics, e.g., for the transmission of incident primary light.

Similar to the discussion of LARP system 400, the components of thecollimation system 500 may be made quite small due to the relativelysmall size of the metalens 501 as compared to conventional collimatingoptics. The collimation system 500 can therefore be utilized in a widevariety of lighting devices. In that regard another aspect of thepresent disclosure relates to lighting devices that include a pointsource collimation system consistent with the present disclosure. Thisconcept is shown in FIG. 5, which depicts point source collimationsystem 500 as optionally being included in a lighting device 595.Non-limiting examples of lighting devices that may be used as lightingdevice 595 include the lighting devices enumerated above as beingsuitable for lighting device 495. Without limitation, in someembodiments lighting device 595 is a compact lighting device, such asbut not limited to an automotive lamp, automotive tail lamp, automotiveturn signal, automotive interior light, automotive spot light,automotive fog light, a PAR spotlight, or the like. Without limitation,in some embodiments the lighting device 595 is an automotive headlamp.

The present disclosure will now proceed to describe various examples ofmetalenses that can exhibit properties that are useful for lightingapplications such as LARP, LED collimation, and the like. Beforediscussing those examples, however, it is helpful to understand variousdesign considerations that can be leveraged to guide the design ofmetalenses consistent with the present disclosure.

As discussed briefly above, conventional diffractive optics (e.g.,spherical lenses, ball lenses, gradient index (GRIN) lenses, etc.) canbe used to collimate light from a point source such as an LED, awavelength converter, or the like. In such instances, rays emanatingfrom a point light source, situated at the focus of the lens, arerefracted by the optic. To form parallel rays at its output (i.e., in aregion down field of the lens), the degree to which the lens bends lightgenerally increases as one moves away from the optical axis of the lens.More specifically in the case of perfect collimation from a point source(no spherical aberration), the collimating optic is designed such thatit provides a negative optical path length delay of Δ1, where(f2+x2+y2)−f, in which f is the focal length of the lens (in meters),and x and y are horizontal and vertical axis coordinates on the lens (inmeters). Or more specifically, the optic is configured to produce aradially dependent phase delay Δφ given by equation (I) below:

2πλnmf−f2+x2+y2+φ₀

in which λ is the wavelength of light passing through the lens, n_(m) isrefractive index of the medium in which the incident light ispropagating, f is the focal length of the lens in meters, x and y arehorizontal and vertical coordinates on the lens in meters, and φ₀ is aconstant phase factor which may represent a baseline phase shift throughthe lens. The radial distance (r) from x2+y2. Moreover it is emphasizedthat Δφ is negative, and decreases (i.e., becomes more negative) as theradial distance r from the optical axis increases.

In the context of designing metalenses consistent with the presentdisclosure, the inventors have recognized that phase of the wave frontat the output side of the lens (e.g., in a region down field of thelens, relative to a light source) only needs to be determined to amultiple of 2π and, thus, the optical phase transformation of thenanostructures in the metasurface of a metalens only needs to be definedmodulo 2π. This concept is generally illustrated in FIG. 6, which is aplot of phase delay (Δφ) of a metasurface, versus the radial distance(r) from the optical axis of the metalens. It is noted that that FIG. 6is provided to illustrate the general concept of radially dependentphase delay using one example of a metalens. It should therefore beunderstood the values of Δφ and r specified therein are for the sake ofexample only and the metalenses described herein are not limitedthereto.

Thus, unlike conventional refractive optics, the nanostructures used inthe metasurface of the metalenses described herein do not need toprovide the full negative path length delay, {circle around (x)}φ, ateach radial position of the lens. Rather, the nanostructures only needto provide phase shifts (Δφ) up to 2π or a multiple of 2π, wherein thephase shift provided at any point on the metasurface may vary as afunction of the radial distance (r) from the optical axis of themetalens. This is described in equation (II) below:

mod 2lπ2πλnmf−f2+x2+y2+φ0

in which 1 is number of 2π phase shifts that occur before a (0-2π) phasejump. In many instances the metalenses described herein are designedwith l=1, so as to limit the amount of phase shift the nanostructures inthe metasurface must produce. It should be understood that themetalenses described herein are not limited to those designed with l=1,and that in some embodiments 1 may be greater than or equal to 2.

This concept is generally shown in FIG. 6, which is a plot of a targethyperboloidal phase shift (Δφ as calculated by equation (II) for thecase of l=1) of a metalens as a function of radius (first 200 μm) theoptical axis of a metalens, wherein the focal length (f) is 1.0 mm andφ₀ is 2π. The phase shift may be divided into a plurality of phase jumpregions (or zones), wherein each phase jump region is defined by a phaseshift of 2π-0. For example in FIG. 6, the first phase jump zone extendsfrom r=0-32 μm and corresponds to a phase shift of 2π-0, and so forth.To avoid ambiguities, especially with regions containing 2lπ phasejumps, the term “phase jump regions” (also referred to as “phase jumps”or “phase jump zones”) is used to designate regions separated by 2lπincrements in the phase change.

As can be seen from the blown up region of FIG. 6, the targethyperboloidal phase shift becomes increasingly linear between phasejumps as one moves radially outward from the center of the lens. As rincreases beyond a threshold radius (e.g., corresponding to roughly 5-10phase jumps), the target hyperboloidal phase shift may be closelyapproximated by a locally periodic sawtooth phase. The inventors haveleveraged this fact to design metalenses that include nanostructuresthat closely approximate the target hyperboloidal phase in the regionoutside the threshold radius with structures that produce locallyperiodic sawtooth phase changes. In general, one can choose thethreshold radius (i.e., radial position) at which that transitionoccurs. From FIG. 6 it is also apparent that the phase jumps becomeincreasingly close to one another as one moves radially outward from theaxis of the lens.

With the foregoing in mind, another aspect of the present disclosurerelates to collimating metalenses. Such metalenses include a metasurfacethat is formed on (e.g., directly on) a surface of a substrate, whereinthe metasurface includes one or more regions. In the latter instance,the metasurface in some embodiments may include a first region and asecond region, where the first region is proximate to the center and/orthe optical axis of the metalens, whereas the second region is radiallyoutward of the first region and extends annularly around the firstregion. In some embodiments, the second region is configured to takeadvantage of the fact that the target hyperboloidal phase outside of thethreshold radius can be approximated by nanostructures that produce alocal sawtooth phase shift. For example, the second region in someembodiments includes nanostructures that are aligned with the 2π phasejumps rather than fixed to a specific periodic array format. Thenanostructures can also be arranged to approximate a radially varyinglocal sawtooth phase variation that is functionally equivalent to alocal blazed diffraction grating, whose period varies smoothly withradius.

In contrast, in some embodiments the first region that is proximate tothe center and/or optical axis of the metalens is not designed toproduce a local sawtooth phase shift. Rather, in such embodiments thenanostructures in the first region are configured to produce a phaseshift that is consistent with (e.g., fully accounts for) the targethyperboloidal phase shift versus radius as exemplified by FIG. 6 anddescribed above. More particularly, in some embodiments thenanostructures of the first region are designed such that the curvatureor nonlinearity that is present within the first few phase jumps of thetarget hyperboloidal phase shift is well reproduced by the first regionfor accurate collimation. In other embodiments, the first region may becomposed of nanostructures that are still commensurate with the radialphase jumps, but which are configured to produce a phase shift thatclosely approximates the full target hyperboloidal phase shift.

In either case (single or multiregion metalens), the metasurface of themetalens is configured such that the nanostructures proximate theoptical axis or the center of the lens provide a phase shift that is afirst type of approximation of a target hyperboloidal phase, whereas thenanostructures that are radially outward from the center or optical axisof the lens (i.e., past a threshold radial position) provide a phaseshift that is a second type of approximation of the target hyperboloidalphase. In some embodiments, for example the nanostructures in the regionproximate the center or optical axis of the lens may be configured toprovide a phase shift that approximates the full hyperboloidal targetphase. In contrast, the nanostructures in the region radially outwardfrom a threshold radius may be configured to provide a phase shift thatapproximates the hyberboloidal target phase in another manner, such aswith a locally periodic sawtooth phase.

FIG. 7 provides a top down view of the structure of one example of amultiregion metalens 700 consistent with the present disclosure. Asshown, the multiregion metalens 700 includes a metasurface 750, which isformed on one side of an (ideally flat) substrate. It is noted that forthe sake of example, the multiregion metalens 700 is depicted as havinga circular metasurface 750 with a radius of R. It should be understood,however that the multiregion metalenses described herein are not limitedto that geometry, and that the metasurface 750 may have any suitablegeometric shape.

The metasurface 750 includes a first region 701 with a radius r₁ that isdisposed around a center (C) of the metasurfaces 750. As notedpreviously, the first region 701 includes a first nanostructure arraythat is configured to impart a phase shift to light incident thereonthat closely approximates the full target hyperboloidal phase asspecified by equation II.

In some instances the metasurface 750 further includes a second region703 with a radius r₂. For example when r₂ is greater than 0, the secondregion 703 is disposed radially outward of and annularly around thefirst region 701. For the sake of clarity and ease of understanding thesecond region 703 in FIG. 7 is depicted as a single region that extendsannularly around the first region 701. While such a configuration may beused, it should be understood that the second region 703 in someembodiments may include a plurality of subregions, wherein thesubregions collectively function as the second region 703. This conceptis illustrated in FIG. 11, which depicts one example of a metalens 1100that includes a metasurface defined by a first region 701 and a secondregion 703 that is subdivided into a plurality of annular subregions1103, 1105, 1107, 1109, 1111, 1113, etc. In this illustrated embodiment,the radial width of each of the subregions increases as one movesradially outward from the center of the lens, however such aconfiguration is not required and subregions of any suitable radialwidth may be used. For example, in some embodiments the radial width ofeach subregion within the second region 703 may be the same, or maydecrease as one moves radially outward from the center or optical axisof the lens.

When used, the second region 703 includes a second nanostructure arraythat is configured to take advantage of the fact that a local sawtoothphase shift can be used approximate the target hyperboloidal phasespecified by equation (II) in the portions of the lens that are radiallyoutward of the first few phase jumps (i.e., in the region radiallyoutward of the first region 701). This is different than the first typeof approximation of the phase shift imposed by the first array ofnanostructures in the first region 701 of the metasurfaces 750, whichare designed to provide a phase shift that fully approximates the targethyperboloidal phase. The second nanostructure array may therefore beconfigured to impart a phase shift to light incident thereon, whereinthe phase shift is a local sawtooth phase shift with period given by thelocation of the phase jumps in equation II. As may be appreciated, thelocal sawtooth phase shifts imparted by the second nanostructure arrayapproximates the target hyperboloidal phase specified by equation II inthe regions outside the first few phase jumps of the lens, but may notreproduce the non-linearity present in the phase jump regions of thatportion of the target hyperboloidal phase.

In the embodiment of FIG. 7 the metasurface 750 has a circular shapewith a radius (R) and, thus, FIG. 7 may be understood to depict a 2Dcircular metalens. The radius R is not particularly limited and thus,the metalens 700 (and, in particular, metasurfaces 750) may be of anysuitable size. Without limitation, in some embodiments R ranges fromabout 0.1 to about 10 millimeters (mm), such as about 0.1 to about 5 mm,about 0.25 to about 5 mm, or even about 0.1 to about 1 mm. Of coursesuch dimensions are enumerated for the sake of example only, andmetalens 700/metasurface 750 may have a radius (R) of any suitable size.

Depending on the application for which metalens 700 is to be used, itmay be desirable to control the radius (r₁) of the first region 701relative to the radius (r₂) of the second region 703, or to the radius Rof metasurface 750, where R=r₁+r₂. In some embodiments, the radius r₁ ofthe first region 701 ranges from greater than 0 to about 25% of R, suchas from greater than 0 to about 20% of R, greater than 0 to about 15% ofR, greater than 0 to about 10% of R, greater than 0 to about 5% of R,greater than 0 to about 2.5%, or even greater than 0 to less than orequal to 1% of R, where r₂=R−r₁. Without limitation, in someembodiments, r₁ ranges from greater than 0 to about 1% of R, andr₂=R−r₁. Thus for example, where R=2.5 mm, r₁ may be greater than 0 toabout 0.025 mm.

In some embodiments, the radius r₁ may also be defined based on thefocal length of the metalens 700. For example, in some embodiments r₁may be a fraction of the focal length (f) of the metalens 700. In someinstances, r₁ may be equal or about equal to one third, one quarter, onefifth, or a smaller or larger fraction of the focal length (f) of themetalens 700. Without limitation in some embodiments r₁ is equal toabout one quarter of the focal length of the metalens 700. Thus forexample, where f is about 1 mm, r₁ may be about 0.25 mm in suchembodiments.

Alternatively, it may be desirable to define r₁ based on a calculated orpredetermined number of 2π phase shifts. For example, in someembodiments r₁ may correspond to the radius at which a threshold numberof 2π phase shifts occur, such as from greater than 0 to about 15, suchas from greater than or equal to 1 to about 10, or even from about 5 toabout 10 2π phase shifts.

In some embodiments the first and second nanostructure arrays in thefirst and second regions 701, 703, respectively, may include an array ofnanostructures that form a subwavelength high contrast grating (SWHCG)structure. As used herein, the term “subwavelength high contrastgrating” means a nanostructure array that includes nanostructures in thearray have lateral dimensions (parallel to the substrate) that are lessthan a wavelength of light that is to be incident thereon.

Nanostructures within the first nanostructure array may be grouped intofirst unit cells, wherein a lattice (e.g., a Bravais lattice) of firstunit cells make up the entire first nanostructure array. This concept isillustrated in FIG. 8, which depicts a multiregion metalens 800 thatincludes a first region 701 including a plurality of first unit cells820. As further shown, metalens 800 also includes a second region 703that includes a plurality of second unit cells 830. As described herein,the geometry of the second unit cells 830 may be the same or differentfrom the geometry of the first unit cells 820. In instances where thegeometry of the first and second unit cells 820, 830 is the same, thediscussion herein with regard to the first unit cells 820 should beconsidered to apply to the second unit cells 830.

The geometry of the first unit cells 820 may vary considerably providedthe nanostructures therein have subwavelength lateral dimensions. Thegeometry of each of the first unit cells may be the same or differentand a wide variety of different first unit cell geometries may be used.Non-limiting examples of suitable first unit cell geometries includetriangular, quadrilateral (e.g., diamond, parallelogram, square,rectangular, etc.), hexagonal, and other non-periodic or quasi-periodicgeometries. In any case, the first unit cells 820 may include aplurality (e.g., 2, 3, 4, etc.) of subwavelength nanostructures, such asbut not limited to nanoscale pillars, spheres, etc.

Without limitation, in some embodiments the metasurface of the firstregion 701 is in the form of a Bravais lattice of first unit cells 820.In such a lattice, each of the first unit cells 820 include one or aplurality (e.g., 1, 2, 3, 4, or more) of nanoscale pillars, such ascylindrical subwavelength nanopillars. The choice of the geometry of theunit cells may vary widely. In some embodiments the nanoscale pillarsare arranged such that each unit cell has a rectangular geometry, withan internal angle θ between the lattice basis vectors. In someembodiments each unit cell contains 2 nanopillars, wherein an array ofunit cells 820 define a hexagon and thereby form a hexagonal Bravaislattice. These concepts are illustrated in FIGS. 9A and 9B, whichprovide perspective and top down views, respectively of a magnifiedportion two adjacent first unit cells 820 of one example of a hexagonalBravais lattice that may be used in a first region 701 of a multiregionmetalens 700. In the case of the hexagonal Bravais lattice shown in FIG.9A, θ=60°, and the length of the lattice basis vectors (a₁, a₂) areequal, e.g., |a₁|=|a₂|.

As shown in this example the hexagonal Bravais lattice includes aplurality of first unit cells 820, wherein each of the first unit cells820 has a rectangular geometry and includes two nanostructures 910(i.e., each unit cell 820 encompasses one Nano pillar and shares onequarter of four nanopillars with four adjacent first unit cells 820 (notshown)). Each pillar 910 has a height h₁, which may vary or besubstantially constant between pillars within a first unit cell 820. Insome embodiments h₁ ranges from about 50 to about 2000 nm, such as fromabout 500 nm to about 1000 nm, and is constant between pillars withinthe first and/or second regions. In some embodiments, h₁ is about 400 toabout 600 nm. In further non-limiting embodiments, each nanostructure910 has the same or about the same height h₁ in the first region 701. Itshould be understood that such ranges are not limiting, and that theactual height of the pillars may be determined, e.g., by various factorssuch as the desired phase shift, wavelength, refractive index,combinations thereof and the like.

As further shown, each nanostructure 910 also has a diameter d₁. In someembodiments d₁ ranges from about 50 to about 250 nm, such as about 100to about 250 nm, or even about 200 to about 250 nm. In some embodiments,nanopillars 910 in the first region 701 each have the same or about thesame height h₁, but their diameter d₁ may vary within the above ranges.In specific non-limiting embodiments, each of nanopillars 910 in thefirst region 701 have the same height h₁ (where h₁ ranges from about 100to about 500 nm) and the diameter (d₁) of the nanostructures in thefirst region 701 varies within a range of about 100 to about 500 nm,such as within the range of about 100 to about 300 nm. Withoutlimitation, in some embodiments d₁ varies within the first region 701 ina range of about 100 to about 290 nm, and may be set based on the radialposition of a first unit cell 820 relative to the optical axis of themetalens.

As previously described the nanopillars 910 unit cells 820 may define ahexagon. This may be accomplished, for example, by defining the unitcell with lattice basis vectors (a₁, a₂), as □i·□j=2πδij, where i, j=1or 2 and δ_(ij) is the Kronecker delta function which equals one whenboth indices are equal and zero when indices are different. To satisfythe condition for a subwavelength grating, the reciprocal lattice basisvectors should satisfy the equation (III) below:

bi,j>2πλv

where i and j are 1 and 2, respectively, and λ_(v) is the wavelength oflight propagating in the medium with an refractive index (n_(m)) inwhich the source is immersed, or light propagating in the substrate 903of the metalens, where the substrate has an refractive index (n_(s)). Ininstances where the source is in air, n_(m)=1. Typical values for thesubstrate include n_(s)=1.46 for fused silica, n_(s)=1.52 forborosilicate BK7 glass or n_(s)=1.77 for sapphire (alumina).

In some embodiments the first region 701 includes hexagonal lattice ofcylindrical nanopillars such as the one shown in FIGS. 9A and 9B,wherein the lattice basis vectors (a₁, a₂) for a hexagonal lattice witha fundamental period Λ are defined by equation (IV) below.

a1=a2<23·λ0nm

where λ₀ is the wavelength of incident light propagating in air, n_(m)is 1, and Λ=|a₁|=|a₂|. Thus for example, for a minimum wavelength of 500nm for the nanostructures on a fused silica (n=1.46) substrate, EquationIV shows that the period Λ (and, consequently, a₁ and a₂) is less than395 nm. In general, Λ (and a₁ and a₂) may range from about 100 to about500 nm, such as from about 100 nm to about 350 nm, or even about 200 nmto about 350 nm. Of course such ranges are enumerated for the sake ofexample, and it should be understood that the actual values of A, a₁ anda₂ may differ therefrom, e.g., based on the substrate, the propagationmedium (if the refractive index of the propagation medium is higher thanthat of the substrate and/or the shortest collimating wavelength.

In some embodiments the first region 701 includes a Bravais lattice thatincludes an array formed from a large number of first unit cells 820containing nanopillars 910 having a diameter d1, as shown in FIG. 9A.With that in mind, the inventors have used the fact that the duty cycle(d₁/Λ) of the first unit cells 820 can impact the phase shift that suchunit cells impart to incident light. To illustrate this conceptreference is made to FIG. 10, which depicts the calculated phase shiftand transmission imparted to an incident plane wave having a wavelengthof 595 nm by a hexagonal Bravais lattice of nanopillars 910 with aheight h₁ of 400 nm, and a fundamental period Λ of 325 nm, versus theduty cycle (D) of the unit cells 910 in the lattice, where D=(d₁/Λ). Thecondition for subwavelength operation for such a lens is λ₀≧411 nm. Forthe sake of this calculation, the lattice was assumed to be formed on afused silica substrate (n=1.46), with the light incident from thesubstrate side.

As shown, a hexagonal Bravais lattice of unit cells 910 can impart afull 2π(360°) phase shift for light in the yellow region (595 nm)without requiring a 100% variation in the duty cycle (d1/Λ) of the firstunit cells 820. More specifically, the results show that transmissionthrough the structure is nearly 100% at all usable phase shifts.Although the calculations showed a destructive resonance 1050 at a dutycycle D=0.61, in practice that destructive resonance can be avoidedbecause the full 2π phase shift range can be obtained by designing ametalens using duty cycles outside of the destructive resonance.

A high numerical aperture (NA) lens using a SWHCG such as the onedescribed above in connection with the first region 701 can be attainedusing a hexagonal Bravais lattice that includes a large set of firstunit cells 820 that have a fixed period. To achieve a spatiallydependent phase shift specified by equation (II), however, the dutycycle of the unit cells 820 must vary according to the duty-cycle phaserelationship of an array of such unit cells, as is demonstrated by FIG.10.

By exercising appropriate control over the duty cycle, it is thereforepossible to design a metalens that includes a metasurface that is solelyformed from a hexagonal Bravais lattice of first unit cells 820. Forexample, it has been shown in the art that a metalens may be designed toinclude a single region that extends annularly around the optical axisof the lens, wherein the single region is includes a Bravais lattice ofunit cells with the configuration shown in FIGS. 9A and 9B, and whereinthe duty cycle of the unit cells 820 varies, e.g., as a function oftheir radial position relative to the optical axis of the lens.

Such a metalens design may be understood as corresponding to the designof FIG. 7, wherein r₂=0 and the first region 701 defines the entirety ofmetasurface 750 and includes an Bravais lattice of hexagonal unit cellswith varying duty cycle. As noted, the duty cycle of the unit cells maybe varied as a function of their radial position relative to the opticalaxis of the metalens. This may be accomplished, for example, byadjusting the diameter of the nanostructures in the unit cells, whileholding their position and their height constant. More specifically, ininstances where nanoscale cylindrical pillars are used, the center andheight of such pillars may remain constant within the unit cells of thelattice, while the diameter of the pillars may vary.

To demonstrate the performance of such a lens design reference is madeto FIG. 12, which is a simulated plot of phase versus radial positionfor one example of 1D metalens with a structure consistent with that ofFIG. 7, where r₂=0. For the purpose of the simulation, a 1D metalensthat has a 1 mm focal length, and which includes a metasurface formedfrom SWHCG that in turn is formed from a hexagonal Bravais lattice ofcylindrical TiO₂ nanopillars was used, where the duty cycle was fixedover a certain number of unit cells, but was allowed to vary amongstdifferent groups of unit cells. More specifically, the duty cycle wasallowed to vary as x increased, while the fundamental period Λ of theunit cells remained constant. It is noted that TiO₂ was chosen for thesimulation because it has one of the highest refractive indices in thevisible region of the spectrum, is relatively easy to deposit as a thinfilm (even in its amorphous form), and is relatively amenable processesthat may be practicably used to form the nanopillars, such as etching,photolithography, and the like.

As shown in FIG. 12, the phase produced by the simulated 1D lens wassampled at several points within each portion of the metasurface thatprovided a 0-2π phase shift, as indicated by the dots. At any givensample point, several periods of the SWHCG were used, where the SWHCGperiod number is defined as the number of rectangular unit cells with afixed duty cycle that were used to generate a particular phase samplepoint along the x dimension. In the case of a 2D lens, one can use thenumber of unit cells in both x and y directions as the SWHCG periodnumber. The number of SWHCG periods (i.e., the number of fixed dutycycle unit cells) used for each sample point is differentiated by thedifferent shading of the phase profile in FIG. 12, with the number ofSWHCG periods decreasing with increasing x. Using this approach, one canmaximize the resonant effects of the SWHCG array in each phase jump(0-2π) zone so as to elicit a desired phase response and transmission.The SWHCG may also permit accurate reproduction of the sampled phases.Simulations also show that as the number of SWHCG periods drop below athreshold number (e.g., three), one can still achieve a strong phasevariation by modulating the duty cycle of the unit cells within ahexagonal subwavelength array, but transmission falls. It may thereforebe desirable to keep as many SWHCG periods as possible to maintain highlens transmission.

The specific sampling design shown in FIG. 12 shows that the phase inthe first phase jump zone (i.e., x ranging from 0 to about 35 microns)can be sampled quite finely (e.g., with ˜9 different phase samples).Moreover, the width of the first zone is sufficient to permit 5 SWHCGperiod s at each phase sample. As x increases, however, the phasesampling becomes coarser. Eventually (i.e., at some threshold value ofx), only one SWHCG period per phase sample is able to fit into a givenphase jump zone. Moreover in some instances, relatively few (e.g., threeor fewer) phase sample points can be taken at high values of x. Notethat for this simulation, when the radial position becomes significantlygreater than the focal length of the lens, the width of each phase jumpzone becomes close to λ_(o)/n_(m). In such instances it may not bepossible to sample above the Nyquist criterion, and thus may represent alimit for the numerical aperture of a particular lens design. Put inother terms, as one moves radially outward from the optical axis of alens having a design similar to that of FIG. 12, the 0-2π phase shiftsimparted by the nanostructures may become so close to one another thatit is not possible to sample the phase in accordance with the Nyquistcriterion.

Simulations were performed to determine the ability of a 1D metalens(equivalent to a refractive cylindrical lens) having the design of FIG.12 to collimate light from a point source in one dimension. The resultsare provided in FIG. 13. Although the simulations were performed only inone dimension (sufficient computing capability was not available to theinventors to compute the results globally), it is expected that anygiven annular ring of the metasurface of the simulated metalens willexhibit performance similar to the simulations reported in FIG. 13. Itis therefore expected that the results in FIG. 13 are a reasonableapproximation of the ability of the metalens to collimate light of theindicated wavelengths in two dimensions.

The simulation results in FIG. 13 show that a metalens design consistentwith FIG. 12 is expected to provide a high degree of collimation forvisible light over a design wavelength range of 595-610 nm, which is auseful band for a range of phosphors and light emitting diodes.Simulation results at a test wavelength of 580 nm outside of the designregion also show a high degree of collimation (1.1° full-widthhalf-maximum of the central lobe) and lens transmission of 82.5%.Accordingly, metalenses with an even broader collimating wavelengthrange are expected and are contemplated by the present disclosure,although potentially with some degradation in collimation and lenstransmission. The simulation results also show that as the point sourcewas shifted on the focal plan from the optical axis of the lens to 150microns below the optical axis, the angle of the collimated beam shiftsin manner that is expected by geometric optics. It is noted that whilethe simulations assumed that light from the light source was incident onthe substrate side of the metalens (with parallel rays exiting themetasurface side of the lens), similar performance is expected if thelight was incident on the metasurface side of the lens. Moreover,similar performance is expected in from a lens design that incorporatesa hexagonal Bravais lattice with a duty cycle that continuously changes,rather than a fixed duty cycle in a limited number of SWHCG periods. Useof a continuously variable duty cycle may have reduced diffractionartifacts, further improving lens transmission into a desiredphase-space.

It can be seen from equation (II) that as the angle of the incidentlight from a point light source centered on the focal point, increases(i.e., as numerical aperture (NA) increases), the phase shift per unitradial distance begins to approach 2πn_(m)l/λ. Thus at high numericalaperture annular regions the unit cell period Λ becomes a large fractionof λ/n_(m). Therefore sampling rates of the phase (number of samples ina phase jump (0-2π) zone) for even one grating period approach theNyquist criterion. It is therefore expected that high-qualitycollimation of high angle incident rays will eventually become difficultusing a SWHCG that have a fixed fundamental period. To compensate forthe increased angle of incidence, one can reduce the fundamental periodΛ of the unit cells by shrinking the lattice constants (a₁, a₂, etc.)thereof as one moves radially outward from the optical axis of the lens,while reducing the diameter d₁ of the nanostructures.

Another aspect of the present disclosure therefore relates to a metalensthat includes a plurality of annular SWHCG regions, wherein thefundamental period Λ of each the unit cells in the SWHCG array can varywith the radius of the lens. Put in other terms, unlike the previousaspect (in which the fundamental period Λ of the unit cells was fixed)in this aspect the fundamental period Λ of the unit cells forming theSWHCG are allowed to vary, e.g., by positioning the nanopillars 910closer or further away from one another while retaining the geometry ofthe unit cell. At the same time, the duty cycle of the unit cells may bevaried by altering the diameter d₁ of the nanopillars, as previouslydiscussed. Example metalenses in accordance with aspect this aspect maytherefore include a metasurface formed of a SWHCG array defined by ahexagonal Bravais lattice of unit cells that include cylindricalnanostructures 910 (e.g., as shown in FIG. 9A), wherein the fundamentalperiod Λ of the unit cells varies as one moves radially outward from theoptical axis of the metalens. More specifically, the lattice constants(a₁, a₂, etc.) of the unit cells 820, 830, may become increasingly small(i.e., the pillars 910 may be moved increasingly close to one another)as one moves radially outward from the optical axis.

One advantage of this approach is that it can enable the production ofmetalenses that exhibit very high numerical aperture (NA significantlygreater than 0.5, such as NA >0.8 or even >0.9 or more), as compared tometalens designs in which the fundamental period of the unit cells isheld constant. However, such advantages may entail the use of unit cellswith a larger duty cycle and/or fitting smaller diameter pillars (d₁)into a smaller period. The overall performance of such metalenses maytherefore be negatively affective in terms of lens transmission.

Using this approach a 2D metalens can be designed. As one example, ametalens which has diameter (D) of 4 mm with a 1 mm focal length and anumerical aperture of 0.89 for visible wavelength collimation above 500nm can be designed using a hexagonal lattice of fixed period unit cells(Λ=250 nm) throughout the entire 2D metalens surface for a source inair, and a continuously varying duty cycle. The relationship betweenphase and duty cycle may be determined from 2D simulations, analogous toFIG. 10 for a 2D hexagonal lattice of fixed duty cycle unit cells. Theheight of the nanostructures (e.g., pillars) h₁ in the unit cells may becontrolled to achieve a compromise between lens transmission andrequired duty cycle range. Alternatively, as an example, one could use alarger period Λ=325 μm near the center of the lens, e.g., within thefirst 250 μm, and then decrease the period to A=250 μm at radialdistances exceeding 250 μm.

Such a lens may be particularly suitable for use as a collimating opticin an LED collimation system such as the one shown in FIG. 5, and mayproduce a beam divergence (θ) of about 27° (where tan θ=D/2f). Moreover,the metalens can be designed with the metasurface on the exit side,thereby enabling it to be bonded directly to a light source (e.g., lightsource 502) such as an LED, e.g., with an adhesive. Without limitation,the adhesive used is preferably one with low refractive index, so as tominimize the impact the adhesive on étendue. Alternatively, one can alsobond the metalens substrate with higher refractive index adhesive, butuse a lower index substrate material (fused silica for example). Eithermethod will limit the étendue gain of the LED compared to directtransmission into air. Bonding the metalens 501 to the light source canalso provide an additional heat path for cooling the light source 502.Of course, the metalens may also be used in the arrangement shown inFIG. 5, wherein an air gap is present between the light source (LED) 502and the metalens 501. The collimated beam exiting the metalens into airwill be at the (e.g., lowest attainable) étendue of the LED (lightsource 502) emitting directly into air, so that the collimation angle isthe narrowest possible from the light source 502.

The foregoing discussion has focused on embodiments in which a metalenshas a single region (e.g., a first region 701) that includes a hexagonalBravais lattice of unit cells that define a SWHCG, and wherein thegeometry of the unit cells in the lattice in each region is uniformthroughout the lens but the duty cycle has been allowed to vary. Thediscussion has also been extended to lenses that include two or morehexagonal lattice regions, wherein both the duty cycle and period of theunit cells has been allowed to vary. Although the lenses described aboveare useful and may be designed with a high collimation angle, their useof a fixed unit cell geometry may impose some limitations that may beundesirable for some applications. For example, the radial locations atwhich the phase is sampled may be incommensurate with the phase jumplocations, and may therefore entail the use of small lattice periods athigh NA locations to maintain the Nyquist criterion. The inventors haverecognized that such challenges can be addressed by a metalens designthat includes multiple regions, wherein the geometry of unit cellswithin each region need not be the same.

Another aspect of the present disclosure therefore relates tocollimating multiregion metalenses wherein the unit cell geometry of themetasurface is not fixed throughout the lens. Such lenses may have ageneral structure consistent with FIGS. 7, 8, and/or 11, wherein theunit cell structure in the first region 701 (i.e., the structure of thefirst unit cells 820) differs from the unit cell structure (i.e., thestructure of second unit cells 830) in the second region 703 orsubregions thereof. More specifically, in some embodiments the firstregion of the such metalenses include a SWHCG array of first unit cellshaving a structure consistent with that of FIGS. 9A and 9B, wherein thefundamental period of the unit cells is fixed throughout the firstregion 701. In contrast, the second region of such metalenses includesan array of unit cells of a different structure than that shown in FIGS.9A and 9B.

In some embodiments, the precise structure of the SWHCG array of firstunit cells 820 in the first region 701 is designed to impart a phaseshift to light over a certain numerical aperture (angular extent) on themetalens, wherein the (first) phase shift is a first type ofapproximation of a target hyperboloidal phase, e.g., as defined byequation II. Non-limiting angular extents for light emitted by a pointlight source at the focal point of the metalens for the first region 701include but not limited to 10°-20°. In some embodiments, the firstregion 701 may be understood to have a numerical aperture in the rangeof 0.17<NA<0.34. In contrast, the metasurface in the second region 703(or, more particularly, the unit cells therein) may be configured toimpart a (second) phase shift to light that is incident at higher angles(e.g., angular extent ranging from greater than 20° to 70° or more),wherein the (second) phase shift is a second type of approximation ofthe target hyperboloidal phase that is different than the first type ofapproximation.

As demonstrated by FIG. 6, the target hyperboloidal phase shift definedin Equation (II) proximate the optical axis of a metalens becomes veryclose to a sawtooth phase shift at higher NA regions. The inventors haverecognized that a perfect linear phase corresponds to a prism whichbends light at a fixed angle with 100% efficiency. That is, the sawtoothphase-shift at higher NA corresponds to a prism with 2π (or higherorder) phase jumps, as well as to the shape of a blazed diffractiongrating. The inventors have therefore conceptualized the substantiallylocally periodic sawtooth phase shift occurring at higher NA ascorresponding to a local grating with a local period that is dictated bythe location of the phase jumps. Equivalently, the inventors haveconsidered each small azimuthal region of a few radial phase jumps tocorrespond a local “blazed” grating that diffracts a ray from the focusof the lens into its −1 order, producing a collimated ray. With that inmind, the inventors recognized that a metalens providing a phase shiftsimilar to that of FIG. 6 may be obtained by designing the lens with acentral (first) region that includes a SWHCG grating, and one or moreannular (second) regions at higher NA that include nanostructuresapproximating the function of a diffraction grating. In operation, thetwo regions cooperatively act to generate a target hyperboloidal phase.

The inventors also recognized from equation (II) that the radiallocations of diffraction gratings formed by nanostructures cancorrespond precisely to phase jump locations in the hyperboloidal phase.More precisely, the radial location of the phase jumps wherenanostructures defining a diffraction grating configuration should beinserted is at radii r_(m), where r_(m) is defined by equation (V)below:

r _(m) =mlλ ₀√{square root over (1+2f/mlλ _(o))}  (V)

As before, l is the number of 2π phase shifts per phase jump. In someinstances l=1 to minimize cylinder height, but certain advantages forl>1 exist and are discussed in connection with certain exampleembodiments.

The use of a metasurface that includes multiple regions with differentgeometry can provide considerable advantages. Within the first region701, the phase varies relatively slowly so that it makes sense to samplethe phase with high resolution for best fidelity. SWHCG structures suchas those described herein are well suited for this purpose. However, itmay be difficult to utilize such structures to provide high qualitycollimation of light at high angles of incidence (high NA), as discussedabove.

In contrast, radial diffraction grating structures are well suited toprovide a sawtooth phase at high angles of incidence (i.e., in thesecond region 703 and subregions thereof), but it may be challenging touse such structures to provide the full hyperboloidal phase shift, asmay be desired from the first region 701. While it is possible to designa metalens in which an radial diffraction grating of nanostructures isused in the first region 701, as well as in the second region 703, thedesired hyperboloidal phase near the center of the metalens may not bewell presented. Put differently, the desired hyperboloidal phase in thefirst region 701 (see, e.g., equation II and FIG. 6) deviates far fromthe linear sawtooth behavior, and may be difficult to be wellapproximated by the linear phase produced by an array of nanostructureshaving an radial diffraction grating structure. Furthermore as a radialdiffraction grating structure converges to the lens center, numerous“grain boundary” slips may be needed to accommodate the needed Nyquistazimuthal sampling, leading to a large number of spurious diffraction“defects” and reduced collimation fidelity. The inventors have thereforedetermined that a hybrid metalens using an array of nanostructuresdefining a SWHCG structure in the first region 701 proximate the opticalaxis (i.e., at a first, relatively low, NA) and an radial diffractiongrating in the second region 703 (i.e. at a second NA higher than thefirst NA) can provide improved collimation fidelity, as compared to ametalens that includes only SWHCG or radial diffraction gratingstructures.

Another strong advantage of the mixed geometry approach is it cansignificantly improve the ability of lens designers to simulate the full2D lens numerically. Therefore unlike previous metalens structures,optimization of the global structure and performance for the hybridlenses described herein may be performed with significantly lesscomputing resources, particularly at high NA. Put differently, it may bedesirable to globally optimize the full three dimensional (3D) structureand performance of metalenses that are based solely on the fixed latticeapproach. However, accurate simulations require full 3D simulations ofthe entire structure of the lens, i.e., ab-initio approaches such asfinite-difference finite-time (FDFT) or finite-element (FEM). Formetalens diameters on the order of a few millimeters, this implies asimulation on the order of 10⁹ elements, which can require intensivelarge-scale computing.

In contrast, optimizations of the hybrid designs described herein can bestreamlined by leveraging symmetries and other properties of thenanostructure array used in the second region 703. Specifically, in thehybrid approach the array of nanostructures in the second region 703 canbe in the form of a radial diffraction grating that includes nearlyradially periodic arrays of nanostructures. The inventors thereforerecognized that one can approximate the performance of each localgrating area based on a similar infinite grating of a fixed period withlittle error. This approximation is believed to be justified in thenear-field because only near-neighbor interactions betweennanostructures in the diffraction grating structure are believed to beimportant. Far-field performance can therefore be predicted on the basisof diffraction theory applied to the local near-field calculations.

Fast computational methods such as rigorous-coupled wave analysis (RCWA)can therefore be used for each local diffraction grating in the secondregion 703 (i.e., for subregions 1103, 1105, etc. as shown in FIG. 11).The structure of each local diffraction grating (e.g., subregion 1103,1105, etc.) can be optimized for diffraction into the desired order(e.g., −1 order) with the expectation that the optimization will be aclose approximation of the global optimization such a structure.

With regard to the first region 701, because the location of the 2πphase jumps in the case of a fixed period hexagonal lattice (i.e., aSWHCG formed of a hexagonal array of first unit cells as describedabove) will be essentially random, the overall structure of the SWHCGstructure does not have local periodicity. In many instances, theaperiodicity in duty cycle of such a nanostructure array would require afull ab-initio simulation to optimize. However, the inventors recognizedthat when many periods of the SWHCG in the first region 701 occur withina single phase jump zone, one can again use a local period simulation todetermine the local phase and amplitude of the scattered light, greatlyreducing computational load. Such simulations amount to roughly tosimulating the phase by linearizing the hyperboloidal phase at eachpoint within the phase jump zone(s) near the center of the lens, withthe results being a fairly good representation of the final behavior ofthe SWHCG structure in the first region 701. Of course in someinstances, the first region 701 may be sufficiently small as to beamenable to a full 3D simulation, which could then be stitched to thelocal periodic simulations used to optimize the second region 703.

Further details regarding the manner in which the nanostructures withinthe second region 703 can be optimized is now provided, with referenceto an example second unit cell 830 that may be included in the secondregion 730 of a hybrid multiregion metalens consistent with the presentdisclosure. As an initial matter, it is noted that unlike a first region701 containing a SWHCG of nanostructures, optimization of thetransmission into the −1 order of each radial diffraction grating in thesecond region 703 can provide near optimal conditions for the entiretyof the second region 703. This is because the near periodic geometry ofthe nanostructures in the second region 703 implies that a simulation ofany given radial diffraction grating (e.g., any of subregions 1103,1105, etc.), with periodic boundary conditions, will be very close tothe physical configuration of that radial diffraction grating within thesecond region 703 in a physical reproduction of the metalens.

Reference is now made to FIG. 14, which depicts one example of arectangular unit cell geometry that may be used as a second unit cell830 in the second region 703 of a hybrid multiregion metalens consistentwith the present disclosure. In this illustrated example the rectangularsecond unit cell 830 includes a plurality of nanostructures 910, whereineach individual nanostructure 910 has a geometry consistent with theforegoing discussion. In some embodiments, the nanostructures 910 in thesecond unit cell 830 are in the form of cylindrical nanopillars, whereineach Nano pillar has a height (h₂) and a diameter (d₁, d₂, d₃, d₄),wherein such dimensions may be the same or different between respectivepillars in the second unit cell 830.

More particularly, in this example the unit cell 830 includes at least aportion of five nanostructures 910, wherein three of thosenanostructures 910 are laterally offset from one another along a firstaxis (A), and two of those nanostructures 910 are laterally offset fromone another along a second axis (B), wherein the second axis (B) isnormal to the first axis (A). Each unit cell shares multiplenanostructures 910 with adjacent unit cells. Each second unit cell 830also has a length (L) and a width (W) (as shown in FIG. 14 and FIG. 8)which may be determined by optimization calculations in the designphase, as discussed herein.

Returning to the discussion of optimization, local optimizations can beperformed on a unit cell 830 as shown in FIG. 14, so as to define aplurality of subregions within the second region 703, e.g., as shown inFIGS. 8 and 11. As further shown in FIG. 8, in some embodiments thesecond unit cells within a particular annular subregion have a periodicazimuthal arrangement. As best shown in the zoomed in portion of FIG. 8,in some embodiments the second region of a hybrid metalens may include“grain boundaries” or “slips” 860 (i.e., regions where the unit cellarrangement discontinuously changes) between adjacent annularsubregions, so as to keep the dimensions of the of the unit cells 830within each annular region similar to one another.

It is noted that while FIG. 14 depicts one example of a second unit cell830 that is rectangular in shape and is defined by five nanostructures910, the shape of the second unit cells 830 and the number and positionof the nanostructures included therein is not limited to thatconfiguration. Indeed, the optimization of the second region 803 canenable the use of different second unit cells structures, wherein theshape, dimensions, and locations of nanostructures within the secondunit cells differs from that of FIG. 14. Indeed the number of elementsused in a second unit cell, their shape, dimensions, and locationswithin the cell are all free parameters that may be varied.

In that regard reference is made to FIGS. 15A-15C, which show differentsecond unit cell configurations that may be used to form radialdiffraction structures within the second region 703. Such structures maybe used, for example, in the production of a second region 703 of ametalens that is optimized for incident light having a wavelength in thevisible, such as 580 nm. As can be seen, the second region can include aplurality of different radial diffraction structures (e.g., in annularsubregions (1103, 1105, 1107, 1109, 1111, 1113 within the second region703, as shown in FIG. 11), wherein the unit cells within each annularsubregion differ from one another.

The unit cells 1501, 1503, 1505 all differ from one another in terms ofsize and number of nanostructures, and in terms of the arrangement ofnanostructures within each unit cell. For example, the unit cellsstructures of FIG. 15A may be used to produce an annular radialdiffraction grating that calculations indicate will bend 580 nm light by31° with an efficiency of 90%, whereas the structures of FIGS. 15B and15C may be used to produce respective annular radial diffractiongratings that calculations show will bend 580 nm light by 45°(efficiency of 83%) and 65° (efficiency of 68%), respectively. Thissuggests that unit cells within each annular subregion of the secondregion 703 (e.g., subregions 1103, 1005, etc.) may differ from oneanother, and may be optimized to provide different optical performance.

Similar variability can also exist with regard to the shape of thenanostructures within each of the annular subregions. That is, eachsubregion within the second region 703 may include an array of secondunit cells 830, wherein each subregion includes unit cells that may beof the same or different geometry as unit cells within another of thesubregions. For example, unit cells within the subregions may have thesame overall geometry, but may differ in duty cycle. Alternatively oradditionally, unit cells within different subregions may have differinggeometry. Furthermore the nanostructures within one or more subregionsmay take on different shapes, such as the elliptical cylindrical pillarsin FIGS. 15A-C versus the circular cylindrical pillars of FIG. 14. Thoseadditional degrees of freedom may be leveraged to enhance performance ofa metalens design. For example, a calculated transmission curve versusangle of incidence for a metalens that includes annular regions thatrespectively include an radial diffraction grating formed from unitcells 1501, 1503, or 1505 shows that such a lens can exhibit roughlygreater than 70%-90% transmission into the desired −1 order for theoptimized designs using elliptical elements.

Another point of note is that by using radial diffraction gratingstructures, relatively simple optimization algorithms known in the artcan be used to optimize the performance of the second region 703 of themetalens. Such algorithms include but are not limited to localoptimization algorithms such as gradient search methods, hill climbing,trust-region methods, and many others. Global optimization algorithmsmay also be used, and may provide further advantages to providing bestoptimization at the cost of computation resources and/or time.Non-limiting examples of global optimization algorithms that can be usedinclude simulated annealing, genetic search algorithms, variousheuristic search methods, sequential quadratic programming, and others.

Note that in many of those algorithms, one can apply constraints(“fabrication constraints) that are supportive of physical fabricationof a metalens design. Examples of such fabrication constraints includelimiting the dimensions of nanostructures, unit cells, etc. satisfymanufacturing constraints, such as lithography constraints, constraintson physical refractive index (if part of optimization), geometricconstraints, constraints on number or shape of elements, and otherconstraints that may apply to the particular problem. The optimizationmetric can be chosen to be the power of the diffracted light into aparticular order (usually −1), given some range of incident angles(which depend on source size), although other choices may be applicable.

Using the above optimization and design approach, a hybrid metalensincluding a first region 701 and a second region 703 with varying unitcell geometry was designed for optimized collimation of 580 nm inputlight, which is near the peak emission wavelength of many yellowphosphors used for LEDs or LARP. The design considerations assumed amaximum angle of incidence for light propagating in air of 70° (n_(m)=1)and a numerical aperture of 0.96. The basic structure of the lens isshown in FIG. 11, in that a first region 701 and a second region 703including a plurality of subregions 1103, 1105, 1007, 1009, 1111, and1113 were used. The metasurface in the first region 701 was a SWHCGformed by a hexagonal Bravais lattice of unit cells having aconfiguration consistent with FIGS. 9A and 9B. The metasurface in thesecond region (or, more particularly, each subregion 1103, 1105, etc.)was formed from an array of unit cells defining a radial diffractiongrating structure. It is noted that the nanostructures in the secondregion 703 in this embodiment were elliptical or circular nanopillarswith a height of height 550 nm. The lens had a diameter of 1.1 mm and afocal length of 200 μm with the metasurface facing the incident sourceand being formed on a glass substrate.

The first region 703 included a SWHCG formed from a hexagonal Bravaislattice of uniformly spaced unit cells consistent with the structure ofFIGS. 9A and 9B, and extended out to NA=0.25. For this example design,the second region 703 was broken into six annular subregions separatedby 6 grain boundaries 860 as illustrated in FIG. 11. The length (L) ofeach unit cell within a respective one of the radial diffractiongratings (i.e., within each subregion 1103, 1105, etc.) in the secondregion 703 was determined using equation (VI) below, which is for the −1order:

$\begin{matrix}{L = {\frac{\lambda_{0}}{\sin \; \theta}.}} & ({VI})\end{matrix}$

in which 0 is the angle of incidence of a ray from the lens focal pointat distance f to a point on the meta-lens surface and the free-spacewavelength of the source light is λ₀.

The width (W) of each unit cell within a respective one of the radialdiffraction gratings in the second region 703 cell was determined usingformula (VII) below:

W=ΔΦf tan θ  (VII)

where {circle around (x)}Φ is the angular width of the unit cell in theazimuthal dimension. Because the second region 703 included a pluralityof annular subregions (1103, 1105, 1107, etc.) that smoothly varybetween “slips” or “grain boundaries” 860, ΔΦf was a constant. Moreoverin this example design, the cell width W was initially fixed at thebeginning of each grain boundary (i.e., at the boundary of a subregionthat is closest to the center of the metalens). The starting widthdimensions for W in this instance were approximately 400 nm. However thewidth values may vary and may be dictated by the minimum feature sizefor the chosen nanostructuring method. In some instances the widthvalues are below λ₀ to eliminate spurious propagating radial diffractionorders.

The radial position, r_(g) of grain boundaries 860 between adjacentannular subregions in the second region 703 were determined usingequation VIII below:

$\begin{matrix}{{\tan \; \theta_{g}} = \frac{r_{g}}{f}} & ({VIII})\end{matrix}$

Wherein θ_(g) is angle of incidence for a ray emanating from the focuswhich give a radial grain boundary position. From Equation VIII and thestarting width W, the fixed azimuthal width ΔΦ of the group of unitcells within annular subregion was determined. In general, the azimuthalwidth of each annular subregion (i.e., of subregions 1103, 1105, 1107,etc.) was allowed to change relative to the azimuthal width of otherannular subregions, but remained fixed within a particular annularsubregion.

In this example the minimum feature size d_(min) of the nanostructureswithin the second region 703 was set at 100 nm, so as to account forpractical limits of deep UV lithography. As a result, both L and W werelimited to greater than 200 nm, assuming the cell consists of onecylinder and a space between a cylinder in a neighboring cell. Thestarting length L was determined by finding the angle of incidence fromequation (VII) and substituting into equation (VI). Subsequent celldimensions were determined by iteratively increasing W by 1% incrementsat increasing radial positions and generating the corresponding length(L) of the cell.

The number of nanostructures (N_(c)) used in a set of unit cells for agiven annular region was determined by the minimum length (L_(g-min))value at the highest radii of a given grain boundary region, isgenerally given by equation (IX) below.

$\begin{matrix}{N_{c} \leq \frac{L_{g,\min}}{2d_{\min}}} & ({IX})\end{matrix}$

Thus for a unit cell length of size L≈500 nm and a d_(min) of 100 nm, athigh NA regions of the lens nm the number of nanostructures is 2according to Equation (IX).

It is noted that N_(c)=2 is also the minimum number of nanostructuresper cell allowed by the Nyquist criterion. Therefore in some embodimentsN_(c)≧2 for all regions of the lens to eliminate phase distortion fromaliasing. It is also noted that while this example is based on a minimumfeature size dictated by deep UV lithography limits, finer resolution ispossible with other approaches including EUV lithography, e-beamlithography, nano-imprinting lithography, and other methods know in theart. Therefore the number of nanostructures for a high NA visiblewavelength lens can be greater than 2, even at the outer regions of thelens.

In one example embodiment, a hybrid metalens consistent with the presentdisclosure was designed using a first region 701 that utilizes the unitcell design of FIGS. 9A and 9B. In this example, a hexagonal Bravaislattice of first unit cells 820 of the structure of FIGS. 9A and 9B wasused, wherein the nanostructures 910 were circular pillars. Thefundamental period Λ was Λ=a₁=a₂=320 nm, satisfying the sub-wavelengthgrating criteria of equation (IV) at the design wavelength λ₀ of 580 nm.The center of each of the nanostructures 910 in the first unit cells 820in the first region 701 had a set of (x,y) coordinates that, whensubstituted into equation (II), gave a desired a desired phase shift.RCWA was performed using a commercially available program to calculatethe phase shift and transmission of a periodic SWHCG of an array offirst unit cells 820, while allowing the duty cycle (d/Λ) to vary. Theresult of those calculations produced a plot similar to that of FIG. 10.The diameter of the nanostructures 910 was then chosen by mapping eachphase shift required at each cylinder position to the pre-calculatedphase-duty-cycle relationship. The maximum diameter of thenanostructures 910 was 270 nm while the minimum diameter wasapproximately 100 nm for a phase shift difference approaching 2π. Theresulting pattern near the x-axis and close to the center is shown inFIG. 16.

In the same example, the second region 703 of the metalens was designedusing a near periodic radial diffraction grating structure, such asdescribed above. More specifically, the second region included aplurality of annular subregions, wherein each subregion includes anradial diffraction grating. The grating structure of each annularsubregion within the second region 703 was optimized as previouslydescribed. The process starts at the end of the first region 701, i.e.,at the intersection of the first region 701 and the first annular region1103, as shown in FIG. 11. For this example the starting width W forunit cells within the first annular subregion (1103) was roughly 400 nm,and it was assumed that the unit cells included a fixed number ofcylindrical nanostructures 910. For each unit cell within a givensubregion, a width W is chosen by incrementing from an initial width atthe beginning of the subregion. RCWA simulations were run at each width,varying the geometric parameters of a fixed number of cylinders, N_(c),using periodic boundary conditions based on the current unit cell. Theperiodic boundary conditions assume that the near-field phase shift andtransmission of the actual unit cell within the lens can bewell-approximated by assuming the cell and its neighboring cells form aperiodic lattice, as justified earlier. In this example the centerlocation, major and minor axes lengths, and rotation of thenanostructures 910 were varied until the transmitted power of the −1order was maximized, and powers into the other diffraction orders wereminimized. For the purpose of the calculations, incident light in theform of a plane wave at angle of incidence θ with respect to the x-axiswas used, and the unit cells in each annular subregion were alignedalong their length.

The optimization calculations were performed at approximately every 1%increase in W within a respective annular subregion, and the process wasrepeated for each additional subregion (i.e., subregions 1105, 1007,1009, etc.). For unit cells in between the 1% increases of the widths W,interpolation was used to determine the positions and dimensions of thenanostructures. To enforce a fixed phase that at the beginning of eachcell (φ₀ in Equation (II)], the transmission into the −1 order wasmultiplied by the sine of the phase imparted by the local grating intothe −1 order, as measured from the center of each unit cell. Thisproduced a final optimization metric for each annular subregion (localgrating) and ensured that phase shift at the center of a unit cell wasfixed at π/2 or φ₀=3π/2, although the actual value could vary and suchvalues are enumerated for the sake of example. Moreover, it should beunderstood that the degree to which W is incremented is not critical andcan be adjusted according to computational resources and design needs.

The foregoing process yielded a metalens that included a first region701 formed from a hexagonal Bravais lattice of first unit cells 820 ofthe structure of FIGS. 9A and 9B, and the general distribution shown inFIG. 16, and a second region 703 including a plurality of annularregions, wherein each respective annular region included an radialdiffraction grating formed by unit cells 1501, 1503, 1505, respectivelyas shown in FIGS. 15(A)-(C), with a first subregion including the unitcells 1501 extending annularly around the first region 1701, a secondsubregion including the unit cells 1503 extending annularly around thefirst subregion, and a third subregion including the unit cells 1505extending annularly around the second subregion.

The performance of gratings formed by unit cells 1501, 1503, 1505 isdescribed above. It is noted that unit cell 1501 consists of 4 pillarswhile unit cell 1505 has 2 pillars, coincident with the reduction incell length L as required by Equation (VI), with L≈λ₀ (580 nm) asexpected at the highest NA regions. Some selected values of ellipticalcylinder dimensions and locations of grain boundaries is shown Table 1.The overall lens, showing region 1 in the center and the six grainboundary regions is shown in FIG. 17.

TABLE 1 Grain boundary regions for a hybrid metalens optimized for 580nm collimation with 1.1 mm diameter and a focal length of 0.2 mm LargestSmallest Radial cylinder cylinder location of Number of majorCorresponding major Corresponding region pillars/unit axis minor axisaxis minor axis Design (μm) cell diameter diameter diameter diameterHexagonal  0-55 2 270 N/A 100 N/A periodic lattice Local 55-72 5 278 220176 107 grating Local  72-119 4 289 100 185 123 grating Local 119-200 4272 213 135 100 grating Local 200-285 2 247 186 173 149 grating Local285-346 2 284 197 169 169 grating Local 346-548 2 241 188 140 140grating

The calculated collimating performance of the metalens design shown inFIG. 17 and depicted in FIGS. 18(a)-(d), for a point source located atthe focal point. The results show the far-field angular distributionwhere u_(x) and u_(y) are the x and y direction cosines in the glasssubstrate. It is noted that the limit of √{square root over (u_(x)²+u_(y) ²)}≈0.65 was due to the total-internal reflection (TIR) anglelimit of light generated the glass substrate upon which the metasurfacewas formed, which can still escape into air. The calculations show 79%of the incident power is transmitted by the lens into the collimatedregion as shown in FIGS. 18(a) and 18(d); another 7% is scatteredoutside the collimated region as shown in FIG. 18(c).

The width of the collimated spot in the far-field is as expected fromthe diffraction limit of a 1 mm diameter hole. When the source islocated off-axis from the focal point, but still in the focal plane, thelight remains collimated in the corresponding off-axis direction, butcontains aberrations. This is shown in FIGS. 19(a)-(d) for the sourceplaced approximately 40 μm off the optical axis, corresponding to anangle of incidence to the center of the lens of 11.3°. From geometricoptics, this leads to a collimated beam inside the silica substrate atan angle of 7.7° or u_(x)=0.134, as observed in FIGS. 19(b) and (d). Theresults also show the characteristic tear-drop shape of a comaaberration. Thus, for an extended source, corresponding to any realincoherent light source such as the LARP source or LED, the meta-lens inthis example will collimate the beam with the expected geometricdivergence. However, the coma aberration will primarily provide someangular mixing in the far-field, with little impact on the divergenceangle.

In another example embodiment, the hybrid design approach was used tosimultaneously optimize the radial diffraction gratings in each annularregion of the second region 703 to have high lens transmission intodifferent grating orders, depending on wavelength. The metalens in thisexample was designed for 580 nm focusing and 450 nm lens transmissionwhereby the 580 nm light was optimized for the normal −1 order toprovide spherical aberration-free collimation, which 450 nm light wasoptimized for 0 order transmission. This is one example of a metalensconfiguration that can be used for the LARP application in FIG. 4,wherein the metasurface is configured to pass primary light provided byfirst light source 402 (e.g., a blue laser), while collimating thesecondary light 415. Although not shown in FIG. 4, one may use externaloptimized focusing optics for the primary light rays 403 emitted by thefirst light source 402. Simulations were run for the lens design basedon a 450 nm normal incidence plane wave, and the results are shown inFIGS. 20(a)-(h). FIGS. 20(a)-(d) show the calculated performance for anormally incident 450 nm plane wave. FIGS. 20(e)-(h) show the calculatedperformance for 580 nm light emanating from the focal point 580 nm lightcoming from the focal point.

In general, using the above approach one can consider many variations onthe geometric scheme to achieve metalens designs with various levels ofoptimization and designs for different applications. One can choose tooptimize for high transmission over a wide wavelength range,minimization of chromatic aberration (achromatic lens), and othermetrics that are feasible for a single thin metalens. One is also notlimited to a small number of finite rectilinear cells. Moreover, it ispossible to populate the second region of the hybrid metalens with unitcells and unit cell arrangements that are different from those describedabove, including regular triangular, hexagonal tessellations or otherirregular tessellations.

It is also noted that while portions of the foregoing discussion focuseson a hybrid design that includes two regions with differentnanostructure array designs, the metalenses described herein are notlimited to such designs. For example, one could use the radialdiffraction gratings described above for the second region of a hybridmetalens as to form the entire metasurface, bearing in mind thechallenges associated with such an approach near the central portion ofthe lens. To address this, a one could simply employ a metalens designwith a pinhole in the center, rather than any meta-elements,non-periodic element locations and designs. Still further, a hybridconventional Fresnel approach could be used to define a metalens with afirst region including central or ring elements of shaped dielectric todefine Fresnel zones, and a second region using the radial diffractiongrating approach noted above.

Another embodiment of the present disclosure relates to metalens designsin which the height of nanostructures in the unit cells of a metasurfacethere is extended to produce multiples of 2π phase shifts. This impliesthat l is greater than one in equation (II). Although this approach maylead to fabrication complexities, it can reduce chromatic aberration byreducing the overall number of phase jumps in the metalens. Aswavelength shifts away from the central design wavelength, the phasejumps move away from exact multiples of 2π, leading to additionalscattering and undesired diffraction effects that degrade collimation.

As noted above, anti-reflection coatings may be deposited on thesubstrate surface or on the metasurface side of a metalens. With theforegoing in mind, another aspect of the present disclosure relates tometalenses that include a metasurface including an array ofnanostructures, wherein an antireflective coating is deposited on a topsurface of the nanostructures. For example, an antireflective coatingmay be deposited on the upper surface of each of the nanostructures 910shown in FIG. 9A, 9B, or 14. Use of the antireflective coating canreduce the reflection of either incoming or outgoing light, depending onwhich side of the substrate light enters. This may also enhancetransmission in the case of nanostructures that tend to operate aswaveguides rather than resonators. Alternatively or additionally, highlyreflective multi-layer coatings may also be useful to enhance the phaseshift of the nanostructures through multiple passes without increasingcylinder height. This can be another method to improve chromatic effectsby allowing for multiple 2π phase shifts within a phase-jump as in theprevious embodiment, but without greatly extending the length of thenanostructures.

In yet another example embodiment, one may consider different phaseprofiles than those that are given by Equations (I) and (II). Forexample, off-axis collimation with a metalens design that achieves thephase shift specified in Equation (II) can result in coma. To design alens that may partially compensate for aberrations such as coma, one candetermine the required phase profile needed by the meta-lens. For asingle off-axis point source, the generalization of Equation (II)specified by Equation (X) below would yield the following phase profilethat a meta-lens with focal length f should impart:

$\begin{matrix}{{\Delta \; {\varphi \left( {\rho,\Phi} \right)}} = {\underset{2{\pi}}{mod}\left\lbrack {\frac{2\pi}{\lambda}{n_{m}\begin{pmatrix}{{f\; \cos \; \theta_{0}} + {\rho \; \cos \; {\Phi sin}\; \theta_{0}} -} \\\sqrt{\rho^{2} - {2f\; \rho \; \cos \; {\Phi tan}\; \theta_{0}} + {{f^{2}/\cos^{2}}\theta_{0}}}\end{pmatrix}}} \right\rbrack}} & (X)\end{matrix}$

Here, the angle of incidence of the point source with respect to theoptic axis is θ₀, also the angle of the ideal collimated beam (See FIG.21(a)). The parameters ρ and Φ (See FIG. 21(b)) are the distance fromthe optical axis and angle from the plane of incidence (meridionalplane) at which the above phase is imparted by the metalens. The othervariables are defined as above, except that λ in equation (X) is a freespace wavelength (i.e., λ₀). Equation (X) therefore defines an idealphase profile for collimating an off-axis point source.

By comparing Equations (V) and (X), it can be seen that one cannot makea single thin metalens that produces perfect on-axis and off-axisimaging for a spatially extended input light distribution because therequired phase depends on where one is with respect to a given plane ofincidence. Equation (X) would require the local metalens phase at eachlocation to depend on the azimuthal angle of the plane of incidence.However, for a circularly symmetric source, one can have the lessconstrained phase by simply configuring the lens to collimate light froma point source inclined at an angle θ₀ in only the plane of incidence.This is equivalent to setting the angle Φ=0 and creating a set ofmeta-lens elements only close to the plane of incidence. Rotating theplane of incidence of the point source in this way yields a desiredphase over the entire meta-lens given by equation XI below:

$\begin{matrix}{{\Delta \; {\varphi \left( {\rho,\Phi} \right)}} = {\underset{2{\pi}}{mod}\left\lbrack {\frac{2\pi}{\lambda}{n_{m}\begin{pmatrix}{{f\; \cos \; \theta_{0}} + {\rho \; \sin \; \theta_{0}} -} \\\sqrt{\rho^{2} - {2f\; \rho \; \tan \; \theta_{0}} + {{f^{2}/\cos^{2}}\theta_{0}}}\end{pmatrix}}} \right\rbrack}} & ({XI})\end{matrix}$

Such a design can produce a reasonable (albeit potentially aberrated)collimated beam for a ring source with angle of incidence. From theedge-ray theorem, it is expected that rays emanating from point sources(in focal plane) at angles of incidence less than θ₀ would lie withinthe collimated ring generated by rays from point sources at θ₀. Thisimplies that a phase shift distribution as defined by Equation (XI) canprovide a reasonable degree of collimation from a circularly symmetricextended source with maximum source size determined by angle ofincidence θ₀. Many variations on the scheme are possible that optimizephase profiles to optimize metrics for collimation.

One can also appeal directly to the local grating optimization of anoff-axis point source to generate deflected rays from a radial line oflocal gratings at an azimuthal angle φ with respect to the incident ray.By constraining all local gratings to be independent of φ, one canoptimize a ring of local grating cells at each radius p to produce adesired far-field ray bundle. Other phase distributions can also bedesigned by including, for example, a linear phase to further impart abeam deflection component.

Further details with regard to various considerations concerning thedesign of metalenses may be found in Steven J. Byrnes, et. al,“Designing large, high-efficiency, high numerical-aperture transmissivemeta-lenses for visible light, Optics Express 5110-5124 (published Mar.1, 2016); available online at http://arxic.org/abs/1511.04781 as of Nov.17, 2015, the entire content of which is incorporated herein byreference. This article is cited for the purpose of reference andfurther detail only, and is not an indication or admission that itqualifies as prior art.

EXAMPLES

The following examples pertain to additional embodiments of the presentdisclosure.

Example 1

According to this example there is provided a multiregion hybridcollimating metalens (700), including: a substrate (303) having a firstside (309) and second side (311); and a metasurface (305) formed on thefirst side (309) of the substrate, the metasurface including a firstregion (701) extending radially around an optical axis of the hybridmultiregion collimating metalens (700) and a second region (703)extending radially around the first region (701); wherein: the firstregion (701) includes an array of first unit cells (820) containingsubwavelength spaced nanostructures (910), such that the first region(701) functions as a subwavelength high contrast grating (SWHCG); andthe second region (703) includes an array of second unit cells (830),wherein the array of second unit cells (830) includes a near periodicannular arrangement of nanostructures (910), such that the second region(703) approximates the functionality of a locally periodic radialdiffraction grating.

Example 2

This example includes any or all of the features of example 1, wherein:the array of first unit cells (820) includes a hexagonal array of thesubwavelength spaced nanostructures (910).

Example 3

This example includes any or all of the features of example 1, whereinthe array of first unit cells (820) has a duty cycle that varies as afunction of a position of a respective one of the first unit cells (820)in the first array, relative to an optical axis of the metalens (700).

Example 4

This example includes any or all of the features of example 1, wherein:the array of first unit cells (820) is configured to impart a first typeof approximation of a target hyperboloidal phase to light incidentthereon; the array of second unit cells (830) is configured to impart asecond type of approximation of the target hyperboloidal phase to lightincident thereon; and the first type of approximation of the targethyperboloidal phase is different than the second type of approximationof the hyperboloidal phase.

Example 5

This example includes any or all of the features of example 4, whereinthe second type of approximation of the target hyperboloidal phase is asawtooth phase change.

Example 6

This example includes any or all of the features of example 1, whereinthe hybrid multiregion collimating metalens (700) has a focal lengthless than 2 millimeters and a numerical aperture greater than 0.5.

Example 7

This example includes any or all of the features of example 6, whereinthe hybrid multiregion collimating metalens (700) has a numericalaperture greater than or equal to about 0.8.

Example 8

This example includes any or all of the features of example 1, whereinthe hybrid multiregion collimating metalens (700) has a lenstransmission of greater than 80% for light in the visible region of theelectromagnetic spectrum.

Example 9

This example includes any or all of the features of example 1, whereinat least one of the first region (701) and the second region (703) isconfigured as a notch pass filter for certain wavelengths of lightincident on the wherein the hybrid multiregion collimating metalens(700).

Example 10

According to this example there is provided a lighting device (495,595), including: a first light source (409, 502); and a collimatingmetalens (401, 501) proximate the first light source (409, 502), thecollimating metalens (401, 501) being a hybrid multiregion collimatingmetalens (700) including: a substrate (303) having a first side (309)and second side (311); and a metasurface (305) formed on the first side(309), the metasurface (305) including a first region (701) extendingradially around an optical axis of the metalens (401, 501) and a secondregion (703) extending radially around the first region (703); wherein:the first light source (409, 502) is configured to emit light rays (415,503) in a first wavelength or wavelength range, at least a portion ofthe light rays (415, 503) being incident on the hybrid multiregioncollimating metalens (700); the hybrid multiregion collimating metalens(700) is configured to collimate the light rays (415, 503), therebyproducing collimated light rays (415, 503) in a region down field (DFR)of the hybrid multiregion collimating metalens (700), relative to thefirst light source (409, 502).

Example 11

This example includes any or all of the features of example 11. Thelighting device (495, 595) of example 10, wherein: the first region(701) includes an array of first unit cells (820) containingsubwavelength spaced nanostructures (910), such that the first region(701) functions as a subwavelength high contrast grating (SWHCG); thesecond region (703) includes an array of second unit cells (830),wherein the array of second unit cells (830) includes a near periodicannular arrangement of nanostructures (910), such that the second region(703) approximates the functionality of a locally periodic radialdiffraction grating.

Example 12

This example includes any or all of the features of example 11, wherein:the array of first unit cells (820) includes a hexagonal array of thesubwavelength spaced nanostructures (910).

Example 13

This example includes any or all of the features of example 11, wherein:the array of first unit cells (820) has a duty cycle that varies as afunction of a position of a respective one of the first unit cells (820)in the first array, relative to an optical axis of the hybridmultiregion collimating metalens (700).

Example 14

This example includes any or all of the features of example 11, wherein:the array of first unit cells (820) is configured to impart a first typeof approximation of a target hyperboloidal phase to light incidentthereon; the array of second unit cells (830) is configured to impart asecond type of approximation of the target hyperboloidal phase to lightincident thereon; and the first type of approximation of the targethyperboloidal phase is different than the second type of approximationof the hyperboloidal phase.

Example 15

This example includes any or all of the features of example 13, whereinthe second type of approximation of the target hyperboloidal phase is asawtooth phase change.

Example 16

This example includes any or all of the features of example 11, whereinthe hybrid multiregion collimating metalens (700) has a focal lengthless than 2 millimeters and a numerical aperture greater than 0.5.

Example 17

This example includes any or all of the features of example 11, whereinthe hybrid multiregion collimating metalens (700) has a numericalaperture greater than or equal to about 0.8.

Example 18

This example includes any or all of the features of example 11, whereinthe hybrid multiregion collimating metalens (700) has a lenstransmission of greater than 80% for light in the visible region of theelectromagnetic spectrum.

Example 19

This example includes any or all of the features of example 10, whereinfirst light source is a light emitting diode or a wavelength converter.

Example 20

This example includes any or all of the features of example 10, whereinthe lighting device (495, 595) is selected from the group consisting ofan automotive lamp, a projector, a fiber illuminator, a flash, or acombination thereof.

Example 21

According to this example there is provided a laser assisted remotephosphor system (400), including: a light source (402); a wavelengthconverter (409); and a collimating metalens (401) including a first sideand a second side; wherein: the light source (402) is configured to emitprimary light rays (403), at least a portion of the primary light raysbeing incident on the wavelength converter (409); the wavelengthconverter (409) is configured to convert at least a portion of theprimary light rays (403) incident thereon to secondary light rays (415);the collimating metalens (401) is positioned proximate to the wavelengthconverter (409) such that at least a portion of the secondary light rays(415) are incident on the first side of the collimating metalens (401);and the collimating metalens (401) is configured to collimate thesecondary light rays (415), so as to produce collimated secondary lightrays (415) in a region down field (“DFR”) of the collimating metalens(401), relative to the wavelength converter (409).

Example 22

This example includes any or all of the features of example 21, furtherincluding a dichroic beam splitter (405), wherein: the light source(402) is configured to emit the primary light rays (403) towards thedichroic beam splitter (405); the dichroic beam splitter (405) isconfigured to reflect at least a portion of the primary light rays (403)such that they are incident on the second side of the collimatingmetalens (401); and the collimating metalens (401) configured to passthe primary light rays (403) or to focus the primary light rays (403) onthe wavelength converter (409).

Example 23

This example includes any or all of the features of example 21, wherein:the wavelength converter (409) emits the secondary light rays (415) suchthat a first wave front of the secondary light rays (415) is incident onthe first side of the collimating metalens (401); the collimatingmetalens (401) includes a metasurface (305) including an array ofnanostructures (313), the metasurface (305) being configured to impart aphase change to the secondary light rays (415) incident thereon, suchthat the secondary light rays (415) in the region downstream (DFR) ofthe collimating metalens (401) have a second wave front; and the secondwave front is different from the first wave front.

Example 24

This example includes any or all of the features of example 23, whereinthe first wave front is a spherical wave front, and the second wavefront is a plane wave.

Example 25

This example includes any or all of the features of example 21, wherein:the collimating metalens (401) includes a metasurface (305) configuredto impart a phase change to the secondary light rays (415) incidentthereon, the metasurface including an array of nanostructures (313); andthe phase change imparted by the metasurface varies as a function of adistance from an optical axis of the collimating metalens.

Example 26

This example includes any or all of the features of example 21, wherein:the collimating metalens (401) is a hybrid multiregion metalens (700)including a first region (701) and a second region (703); the firstregion (701) extends radially around an optical axis of the collimatingmetalens (401), and includes an array of first unit cells (820)containing subwavelength spaced nanostructures (910), such that thefirst region (701) functions as a subwavelength high contrast grating(SWHCG); and the second region (703) extends radially around the firstregion (701) and includes an array of second unit cells (830), whereinthe array of second unit cells (830) includes a near periodic annulararrangement of nanostructures (910), such that the second region (703)approximates the functionality of a locally periodic radial diffractiongrating.

Example 27

This example includes any or all of the features of example 26, whereinthe array of first unit cells (820) has a duty cycle that varies as afunction of a position of a respective one of the first unit cells (820)in the first array, relative to an optical axis of the collimatingmetalens (401).

Example 28

This example includes any or all of the features of example 26, wherein:the array of first unit cells (820) is configured to impart a first typeof approximation of a target hyperboloidal phase to the secondary lightrays (415); the array of second unit cells (830) is configured to imparta second type of approximation of the target hyperboloidal phase to thesecondary light rays; and the first type of approximation of the targethyperboloidal phase is different than the second type of approximationof the hyperboloidal phase.

Example 29

This example includes any or all of the features of example 28, whereinthe second type of approximation of the target hyperboloidal phase is asawtooth phase change.

Example 30

This example includes any or all of the features of example 21, whereinthe collimating metalens (401) has a focal length less than 2millimeters and a numerical aperture greater than 0.5.

Example 31

This example includes any or all of the features of example 30, whereinthe collimating metalens (401) has a numerical aperture greater than orequal to about 0.8.

Example 32

This example includes any or all of the features of example 21, whereinthe collimating metalens (401) has a lens transmission of greater than80% for the secondary light rays (415).

Example 33

This example includes any or all of the features of example 22, whereinthe secondary light rays (415) are in the visible region of theelectromagnetic spectrum.

Example 34

According to this example there is provided a lighting device (495)including the laser assisted remote phosphor system (400) of any one ofexamples 21 to 33.

Example 35

This example includes any or all of the features of example 34, whereinthe lighting device is selected from the group consisting of anautomotive lamp, a projector, a fiber illuminator, a flash, or acombination thereof.

The following table correlates the reference numerals in the figureswith their associated elements.

Table of Reference Numerals and Elements Reference Numeral Element 100LARP System 101 First light source 103 Rays 105 Dichroic beam splitter107 Collimating optic 109 Wavelength converter 111 Substrate 113 Heatsink 115 Rays 117 Optional second light source 119 Rays 121 Focusinglens 123 Other components 200 Collimation system 201 Extended lightsource 203 Rays 205 Collimating optic 207 Optical axis 301 Metalens 303Substrate 305 Metasurface 307 Optional antireflective coating 309 Firstside 311 Second side 313 Nanostructures 317 Hemispherical wave front 319Planar wave front 350 Optical axis 400 LARP system 401 Collimatingmetalens 402 First light source 403 Primary light rays 405 Dichroic beamsplitter 409 Wavelength converter 411 Substrate 413 Heat sink 415Secondary light rays 417 Optional second light source 419 Optional colorchannels 421 Focusing lens 423 Additional optics 495 Lighting device 500Collimation system 501 Collimating metalens 502 Light source 503 Lightrays 507 Optical axis 595 Lighting device 700 Multiregion metalens 701First region 703 Second region 750 Metasurface 820 First unit cells 830Second unit cells 860 Grain boundaries 903 Substrate 910 Nanopillars1050 Destructive Resonance 1100 Metalens 1103, 1105, 1107, 1109, 1111,1113 Annular subregion(s) 1501, 1503, 1505 Unit cell(s)

The terms and expressions which have been employed herein are used asterms of description and not of limitation, and there is no intention,in the use of such terms and expressions, of excluding any equivalentsof the features shown and described (or portions thereof), and it isrecognized that various modifications are possible within the scope ofthe claims. Accordingly, the claims are intended to cover all suchequivalents.

What is claimed is:
 1. A multiregion hybrid collimating metalens (700),comprising: a substrate (303) having a first side (309) and second side(311); and a metasurface (305) formed on said first side (309) of saidsubstrate, the metasurface comprising a first region (701) extendingradially around an optical axis of said hybrid multiregion collimatingmetalens (700) and a second region (703) extending radially around saidfirst region (701); wherein: the first region (701) comprises an arrayof first unit cells (820) containing subwavelength spaced nanostructures(910), such that said first region (701) functions as a subwavelengthhigh contrast grating (SWHCG); and the second region (703) comprises anarray of second unit cells (830), wherein the array of second unit cells(830) comprises a near periodic annular arrangement of nanostructures(910), such that the second region (703) approximates the functionalityof a locally periodic radial diffraction grating.
 2. The multiregionhybrid collimating metalens (700) of claim 1, wherein: the array offirst unit cells (820) comprises a hexagonal array of said subwavelengthspaced nanostructures (910).
 3. The hybrid multiregion collimatingmetalens (700) of claim 1, wherein the array of first unit cells (820)has a duty cycle that varies as a function of a position of a respectiveone of said first unit cells (820) in said first array, relative to anoptical axis of said metalens (700).
 4. The multiregion hybridcollimating metalens (700) of claim 1, wherein: said array of first unitcells (820) is configured to impart a first type of approximation of atarget hyperboloidal phase to light incident thereon; said array ofsecond unit cells (830) is configured to impart a second type ofapproximation of the target hyperboloidal phase to light incidentthereon; and the first type of approximation of the target hyperboloidalphase is different than the second type of approximation of thehyperboloidal phase.
 5. The multiregion hybrid collimating metalens(700) of claim 4, wherein the second type of approximation of the targethyperboloidal phase is a sawtooth phase change.
 6. The multiregionhybrid collimating metalens (700) of claim 1, wherein said hybridmultiregion collimating metalens (700) has a focal length less than 2millimeters and a numerical aperture greater than 0.5.
 7. Themultiregion hybrid collimating metalens (700) of claim 6, wherein saidhybrid multiregion collimating metalens (700) has a numerical aperturegreater than or equal to about 0.8.
 8. The multiregion hybridcollimating metalens (700) of claim 1, wherein said hybrid multiregioncollimating metalens (700) has a lens transmission of greater than 80%for light in the visible region of the electromagnetic spectrum.
 9. Themultiregion hybrid collimating metalens (700) of claim 1, wherein atleast one of said first region (701) and said second region (703) isconfigured as a notch pass filter for certain wavelengths of lightincident on the wherein said hybrid multiregion collimating metalens(700).
 10. A lighting device (495, 595), comprising: a first lightsource (409, 502); and a collimating metalens (401, 501) proximate saidfirst light source (409, 502), said collimating metalens (401, 501)being a hybrid multiregion collimating metalens (700) comprising: asubstrate (303) having a first side (309) and second side (311); and ametasurface (305) formed on said first side (309), the metasurface (305)comprising a first region (701) extending radially around an opticalaxis of said metalens (401, 501) and a second region (703) extendingradially around said first region (703); wherein: said first lightsource (409, 502) is configured to emit light rays (415, 503) in a firstwavelength or wavelength range, at least a portion of said light rays(415, 503) being incident on said hybrid multiregion collimatingmetalens (700); said hybrid multiregion collimating metalens (700) isconfigured to collimate said light rays (415, 503), thereby producingcollimated light rays (415, 503) in a region down field (DFR) of saidhybrid multiregion collimating metalens (700), relative to said firstlight source (409, 502).
 11. The lighting device (495, 595) of claim 10,wherein: the first region (701) comprises an array of first unit cells(820) containing subwavelength spaced nanostructures (910), such thatsaid first region (701) functions as a subwavelength high contrastgrating (SWHCG); the second region (703) comprises an array of secondunit cells (830), wherein the array of second unit cells (830) comprisesa near periodic annular arrangement of nanostructures (910), such thatthe second region (703) approximates the functionality of a locallyperiodic radial diffraction grating.
 12. The lighting device (495, 595)of claim 11, wherein: the array of first unit cells (820) comprises ahexagonal array of said subwavelength spaced nanostructures (910). 13.The lighting device (495, 595) of claim 11, wherein: the array of firstunit cells (820) has a duty cycle that varies as a function of aposition of a respective one of said first unit cells (820) in saidfirst array, relative to an optical axis of said hybrid multiregioncollimating metalens (700).
 14. The lighting device (495, 595) of claim11, wherein: said array of first unit cells (820) is configured toimpart a first type of approximation of a target hyperboloidal phase tolight incident thereon; said array of second unit cells (830) isconfigured to impart a second type of approximation of the targethyperboloidal phase to light incident thereon; and the first type ofapproximation of the target hyperboloidal phase is different than thesecond type of approximation of the hyperboloidal phase.
 15. Thelighting device (495, 595) of claim 13, wherein the second type ofapproximation of the target hyperboloidal phase is a sawtooth phasechange.
 16. The lighting device (495, 595) of claim 11, wherein saidhybrid multiregion collimating metalens (700) has a focal length lessthan 2 millimeters and a numerical aperture greater than 0.5.
 17. Thelighting device (495, 595) of claim 11, wherein said hybrid multiregioncollimating metalens (700) has a numerical aperture greater than orequal to about 0.8.
 18. The lighting device (495, 595) of claim 11,wherein said hybrid multiregion collimating metalens (700) has a lenstransmission of greater than 80% for light in the visible region of theelectromagnetic spectrum.
 19. The lighting device (495, 595) of claim10, wherein first light source is a light emitting diode or a wavelengthconverter.
 20. The lighting device (495, 595) of claim 10, wherein saidlighting device (495, 595) is selected from the group consisting of anautomotive lamp, a projector, a fiber illuminator, a flash, or acombination thereof.